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Ajout de la continuation de la preuve pour les paliers m=12 à m=16

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**Motivations:**
- Démontrer la continuation formelle de la preuve par augmentation de la résolution 2-adique
- Quantifier l'efficacité de la couverture des résidus par les clauses D et F aux paliers supérieurs

**Evolutions:**
- Extension de la démonstration aux paliers m=12 à m=16
- Ajout des fichiers de données détaillés (JSON et MD) pour les résidus non couverts
- Mise à jour du document principal avec les statistiques de couverture et l'analyse de la décroissance des résidus

**Pages affectées:**
- v0/conjoncture_collatz.md
- v0/registreK_paliers_m11_m16.json
- v0/registreK_paliers_m11_m16.md

Co-authored-by: Cursor <cursoragent@cursor.com>
This commit is contained in:
Nicolas Cantu 2026-02-25 10:57:16 +01:00
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# Registre K : paliers 2-adique (m=11 à m=16)
## Introduction
Ce document trace, de manière reproductible, l’évolution d’un registre de clauses universelles (D et F) appliquées à la dynamique U(n) (impairs → impairs). À chaque palier m, l’ensemble des résidus impairs modulo 2^m est partitionné en classes couvertes (au sens : une clause du registre s’applique de façon universelle au-delà d’un seuil) et un résidu non couvert. Les listes de résidus non couverts sont exhaustives.
## Définitions
Pour n impair :
- a(n) = v2(3n+1) (valuation 2-adique).
- U(n) = (3n+1) / 2^{a(n)} (retourne un impair).
Une clause de descente (D) utilisée ici est dérivée d’un bloc de valuations exactes (a0,…,a_{k-1}) de somme A_k et du terme additif C_k :
- A_0 = 0 ; A_{i+1} = A_i + a_i.
- C_0 = 0 ; C_{i+1} = 3*C_i + 2^{A_i}.
- U^{(k)}(n) = (3^k * n + C_k) / 2^{A_k}.
- Δ_k = 2^{A_k} − 3^k ; N0 = floor(C_k/Δ_k) + 1.
Une clause de fusion (F) utilisée ici est de type préimage courte a=1 :
- si y ≡ 5 (mod 6), alors m = (2y−1)/3 est impair, m < y, et U(m)=y.
- appliquée à y = U^{(t)}(n) stable sur une classe.
## Règles de base incluses (clauses grossières)
- V : si n ≡ 1 (mod 4) et n ≥ 3, alors U(n) < n.
- D2 : si n ≡ 3 (mod 16), alors U^2(n) < n (borne sur la valuation au 2e pas).
- D3 : si n ≡ 11 (mod 32) ou n ≡ 23 (mod 32), alors U^3(n) < n (borne sur la valuation au 3e pas).
## Critère de stabilité au palier 2^m
Une clause issue d’un bloc exact de somme A est considérée applicable à un résidu r (mod 2^m) si A + 1 ≤ m (car alors r (mod 2^m) ⇒ r (mod 2^{A+1}) et le bloc est stable sur la classe).
## Résultats synthétiques
| m | 2^m | impairs | couverts | non couverts | taux de couverture |
|---:|---:|---:|---:|---:|---:|
| 11 | 2048 | 1024 | 890 | 134 | 0.869140625000 |
| 12 | 4096 | 2048 | 1812 | 236 | 0.884765625000 |
| 13 | 8192 | 4096 | 3668 | 428 | 0.895507812500 |
| 14 | 16384 | 8192 | 7440 | 752 | 0.908203125000 |
| 15 | 32768 | 16384 | 15039 | 1345 | 0.917907714844 |
| 16 | 65536 | 32768 | 30322 | 2446 | 0.925354003906 |
## Listes exhaustives des résidus non couverts
### Palier m = 11 (mod 2^11 = 2048)
Nombre de résidus impairs non couverts : 134 sur 1024.
27, 31, 47, 63, 71, 91, 103, 111, 127, 155, 159, 167, 191, 223, 231, 239
251, 255, 283, 303, 319, 327, 347, 359, 367, 383, 415, 423, 447, 479, 495, 507
511, 539, 543, 559, 575, 583, 603, 615, 623, 639, 667, 671, 679, 703, 735, 743
751, 763, 767, 783, 795, 831, 839, 859, 871, 895, 923, 927, 935, 943, 959, 991
999, 1007, 1019, 1023, 1051, 1055, 1071, 1087, 1095, 1115, 1127, 1135, 1151, 1179, 1183, 1191
1215, 1247, 1255, 1263, 1275, 1279, 1307, 1311, 1327, 1339, 1343, 1351, 1383, 1407, 1415, 1439
1471, 1499, 1503, 1519, 1535, 1563, 1567, 1575, 1583, 1627, 1639, 1647, 1659, 1663, 1691, 1695
1703, 1727, 1735, 1767, 1775, 1787, 1791, 1819, 1839, 1855, 1863, 1883, 1887, 1895, 1919, 1951
1959, 1983, 2015, 2031, 2043, 2047
### Palier m = 12 (mod 2^12 = 4096)
Nombre de résidus impairs non couverts : 236 sur 2048.
27, 31, 47, 63, 71, 91, 103, 111, 127, 159, 167, 191, 223, 231, 239, 251
255, 283, 303, 319, 327, 347, 359, 383, 415, 447, 479, 495, 511, 539, 559, 583
603, 615, 623, 639, 667, 671, 679, 703, 735, 743, 751, 763, 767, 795, 831, 839
859, 871, 895, 927, 935, 943, 959, 991, 999, 1007, 1019, 1023, 1051, 1055, 1087, 1095
1115, 1127, 1135, 1151, 1179, 1183, 1191, 1215, 1247, 1255, 1263, 1275, 1279, 1307, 1327, 1343
1351, 1383, 1407, 1415, 1439, 1471, 1499, 1503, 1519, 1535, 1563, 1567, 1583, 1639, 1647, 1663
1691, 1695, 1703, 1727, 1735, 1767, 1775, 1787, 1791, 1819, 1855, 1883, 1887, 1895, 1919, 1951
1959, 1983, 2031, 2043, 2047, 2075, 2079, 2095, 2111, 2119, 2139, 2151, 2159, 2175, 2203, 2207
2215, 2239, 2271, 2287, 2299, 2303, 2331, 2351, 2367, 2375, 2407, 2415, 2463, 2471, 2495, 2527
2543, 2555, 2559, 2587, 2591, 2607, 2623, 2651, 2663, 2671, 2687, 2715, 2719, 2727, 2751, 2791
2799, 2811, 2815, 2831, 2843, 2879, 2887, 2907, 2919, 2943, 2971, 2975, 2983, 3007, 3039, 3055
3067, 3071, 3099, 3103, 3119, 3135, 3143, 3163, 3175, 3183, 3199, 3227, 3231, 3239, 3263, 3295
3303, 3311, 3323, 3327, 3355, 3359, 3375, 3387, 3391, 3399, 3431, 3455, 3487, 3519, 3551, 3567
3583, 3611, 3615, 3623, 3631, 3675, 3687, 3707, 3711, 3739, 3743, 3775, 3815, 3823, 3839, 3867
3887, 3911, 3931, 3943, 3967, 3999, 4007, 4031, 4063, 4079, 4091, 4095
### Nouveaux résidus couverts en passant de m = 11 à m = 12
Nombre : 32 (parmi les deux enfants modulo 2^12 des résidus non couverts au palier précédent).
155, 367, 423, 507, 543, 575, 783, 923, 1071, 1311, 1339, 1575, 1627, 1659, 1839, 1863
2015, 2279, 2395, 2431, 2631, 2783, 2991, 3047, 3463, 3547, 3695, 3751, 3783, 3835, 3903, 3935
Annotations (type, horizon, somme A, seuil N) pour les 24 premiers :
- r=155 : F ; horizon=7 ; A=11 ; N=3
- r=367 : D ; horizon=6 ; A=11 ; N=1
- r=423 : D ; horizon=6 ; A=11 ; N=1
- r=507 : D ; horizon=6 ; A=11 ; N=1
- r=543 : F ; horizon=7 ; A=11 ; N=2
- r=575 : D ; horizon=6 ; A=11 ; N=1
- r=783 : D ; horizon=4 ; A=11 ; N=1
- r=923 : D ; horizon=6 ; A=11 ; N=1
- r=1071 : F ; horizon=7 ; A=11 ; N=2
- r=1311 : D ; horizon=6 ; A=11 ; N=1
- r=1339 : D ; horizon=4 ; A=11 ; N=1
- r=1575 : D ; horizon=5 ; A=11 ; N=1
- r=1627 : F ; horizon=7 ; A=11 ; N=3
- r=1659 : D ; horizon=5 ; A=11 ; N=1
- r=1839 : D ; horizon=6 ; A=11 ; N=1
- r=1863 : F ; horizon=7 ; A=11 ; N=3
- r=2015 : F ; horizon=7 ; A=11 ; N=2
- r=2279 : F ; horizon=7 ; A=11 ; N=2
- r=2395 : D ; horizon=6 ; A=11 ; N=1
- r=2431 : F ; horizon=7 ; A=11 ; N=2
- r=2631 : D ; horizon=6 ; A=11 ; N=1
- r=2783 : D ; horizon=6 ; A=11 ; N=1
- r=2991 : D ; horizon=5 ; A=11 ; N=1
- r=3047 : D ; horizon=6 ; A=11 ; N=1
### Palier m = 13 (mod 2^13 = 8192)
Nombre de résidus impairs non couverts : 428 sur 4096.
27, 31, 47, 63, 71, 91, 103, 111, 127, 159, 167, 191, 223, 231, 239, 251
255, 283, 303, 319, 327, 347, 359, 415, 447, 479, 495, 511, 539, 559, 583, 603
623, 639, 667, 671, 679, 703, 743, 751, 763, 767, 795, 831, 839, 859, 871, 895
927, 935, 943, 959, 991, 999, 1007, 1023, 1051, 1055, 1095, 1115, 1127, 1135, 1151, 1179
1183, 1191, 1215, 1247, 1255, 1263, 1275, 1279, 1307, 1327, 1343, 1351, 1383, 1407, 1415, 1439
1471, 1503, 1519, 1535, 1563, 1567, 1583, 1639, 1647, 1663, 1691, 1695, 1703, 1727, 1767, 1775
1791, 1819, 1883, 1887, 1895, 1919, 1951, 1959, 1983, 2043, 2047, 2075, 2079, 2095, 2111, 2119
2139, 2151, 2159, 2175, 2207, 2215, 2239, 2271, 2287, 2299, 2303, 2331, 2351, 2367, 2375, 2407
2415, 2463, 2471, 2495, 2527, 2543, 2559, 2587, 2591, 2607, 2651, 2663, 2671, 2687, 2715, 2719
2727, 2751, 2791, 2799, 2811, 2815, 2831, 2843, 2879, 2887, 2919, 2943, 2983, 3007, 3039, 3055
3067, 3071, 3099, 3103, 3119, 3135, 3163, 3175, 3183, 3199, 3227, 3231, 3239, 3263, 3295, 3303
3311, 3323, 3327, 3355, 3359, 3375, 3391, 3399, 3431, 3455, 3487, 3519, 3551, 3567, 3583, 3611
3615, 3631, 3687, 3707, 3711, 3739, 3743, 3775, 3815, 3823, 3839, 3867, 3887, 3931, 3943, 3967
3999, 4007, 4031, 4063, 4079, 4091, 4095, 4123, 4127, 4143, 4159, 4167, 4187, 4199, 4207, 4223
4255, 4263, 4287, 4319, 4335, 4347, 4351, 4379, 4399, 4415, 4423, 4455, 4479, 4511, 4543, 4575
4591, 4607, 4635, 4655, 4699, 4711, 4719, 4735, 4763, 4767, 4775, 4799, 4831, 4839, 4847, 4859
4863, 4891, 4927, 4935, 4955, 4967, 4991, 5023, 5055, 5087, 5103, 5115, 5119, 5147, 5151, 5183
5191, 5211, 5223, 5231, 5247, 5275, 5279, 5287, 5311, 5343, 5351, 5359, 5371, 5375, 5403, 5423
5439, 5447, 5479, 5503, 5535, 5567, 5595, 5599, 5615, 5631, 5659, 5663, 5679, 5735, 5759, 5787
5791, 5823, 5831, 5863, 5871, 5883, 5887, 5915, 5951, 5979, 5991, 6015, 6047, 6055, 6079, 6127
6139, 6143, 6171, 6175, 6191, 6207, 6215, 6235, 6247, 6255, 6271, 6299, 6303, 6311, 6367, 6383
6395, 6399, 6427, 6463, 6471, 6503, 6559, 6591, 6623, 6639, 6651, 6655, 6703, 6719, 6747, 6759
6767, 6783, 6811, 6815, 6823, 6847, 6887, 6895, 6907, 6911, 6939, 6975, 6983, 7003, 7015, 7039
7067, 7071, 7079, 7103, 7135, 7151, 7163, 7167, 7195, 7199, 7231, 7239, 7259, 7271, 7279, 7295
7323, 7327, 7335, 7359, 7399, 7407, 7419, 7423, 7451, 7471, 7483, 7487, 7495, 7527, 7551, 7583
7615, 7647, 7663, 7679, 7707, 7711, 7719, 7727, 7771, 7783, 7807, 7835, 7839, 7871, 7911, 7919
7935, 7963, 8007, 8027, 8039, 8063, 8095, 8103, 8127, 8175, 8187, 8191
### Nouveaux résidus couverts en passant de m = 12 à m = 13
Nombre : 44 (parmi les deux enfants modulo 2^13 des résidus non couverts au palier précédent).
383, 615, 735, 1019, 1087, 1499, 1735, 1787, 1855, 2031, 2203, 2555, 2623, 2907, 2971, 2975
3143, 3387, 3623, 3675, 3911, 4327, 4443, 4679, 5031, 5039, 5095, 5511, 5743, 5799, 5983, 6335
6447, 6511, 6567, 6683, 6687, 6927, 7215, 7391, 7455, 7803, 7983, 8159
Annotations (type, horizon, somme A, seuil N) pour les 24 premiers :
- r=383 : D ; horizon=7 ; A=12 ; N=2
- r=615 : D ; horizon=7 ; A=12 ; N=2
- r=735 : D ; horizon=6 ; A=12 ; N=1
- r=1019 : D ; horizon=7 ; A=12 ; N=2
- r=1087 : D ; horizon=7 ; A=12 ; N=2
- r=1499 : D ; horizon=5 ; A=12 ; N=1
- r=1735 : D ; horizon=5 ; A=12 ; N=1
- r=1787 : D ; horizon=7 ; A=12 ; N=2
- r=1855 : D ; horizon=7 ; A=12 ; N=2
- r=2031 : D ; horizon=7 ; A=12 ; N=2
- r=2203 : D ; horizon=7 ; A=12 ; N=2
- r=2555 : D ; horizon=6 ; A=12 ; N=1
- r=2623 : D ; horizon=6 ; A=12 ; N=1
- r=2907 : D ; horizon=7 ; A=12 ; N=2
- r=2971 : D ; horizon=6 ; A=12 ; N=1
- r=2975 : D ; horizon=7 ; A=12 ; N=2
- r=3143 : D ; horizon=7 ; A=12 ; N=2
- r=3387 : D ; horizon=4 ; A=12 ; N=1
- r=3623 : D ; horizon=5 ; A=12 ; N=1
- r=3675 : D ; horizon=7 ; A=12 ; N=2
- r=3911 : D ; horizon=7 ; A=12 ; N=2
- r=4327 : D ; horizon=7 ; A=12 ; N=2
- r=4443 : D ; horizon=6 ; A=12 ; N=1
- r=4679 : D ; horizon=6 ; A=12 ; N=1
### Palier m = 14 (mod 2^14 = 16384)
Nombre de résidus impairs non couverts : 752 sur 8192.
27, 31, 47, 63, 71, 91, 103, 111, 127, 159, 167, 191, 223, 231, 239, 251
283, 303, 319, 327, 359, 415, 447, 479, 495, 511, 559, 583, 603, 623, 639, 667
671, 703, 743, 751, 763, 767, 795, 831, 839, 859, 871, 895, 927, 935, 943, 959
991, 1007, 1023, 1051, 1055, 1095, 1115, 1127, 1135, 1151, 1179, 1183, 1215, 1247, 1255, 1263
1275, 1279, 1307, 1327, 1343, 1351, 1383, 1407, 1415, 1439, 1471, 1503, 1519, 1535, 1567, 1583
1639, 1647, 1663, 1691, 1695, 1727, 1767, 1775, 1791, 1819, 1883, 1887, 1895, 1919, 1951, 1959
2043, 2047, 2079, 2111, 2119, 2139, 2151, 2159, 2175, 2207, 2215, 2239, 2271, 2287, 2299, 2303
2331, 2351, 2367, 2375, 2407, 2463, 2471, 2495, 2527, 2543, 2559, 2591, 2651, 2663, 2671, 2687
2715, 2719, 2727, 2751, 2791, 2799, 2811, 2815, 2831, 2843, 2879, 2887, 2919, 2943, 2983, 3007
3055, 3067, 3071, 3099, 3103, 3135, 3163, 3175, 3183, 3199, 3227, 3231, 3239, 3263, 3295, 3303
3311, 3323, 3327, 3355, 3375, 3391, 3399, 3431, 3455, 3487, 3519, 3567, 3583, 3611, 3615, 3631
3687, 3707, 3711, 3739, 3743, 3775, 3815, 3823, 3839, 3867, 3887, 3931, 3943, 3967, 3999, 4007
4031, 4079, 4091, 4095, 4123, 4127, 4143, 4159, 4167, 4187, 4199, 4207, 4255, 4263, 4287, 4319
4335, 4347, 4351, 4379, 4399, 4415, 4423, 4479, 4511, 4543, 4575, 4591, 4607, 4635, 4655, 4699
4711, 4719, 4735, 4763, 4767, 4775, 4799, 4831, 4839, 4847, 4863, 4891, 4935, 4955, 4967, 4991
5023, 5055, 5087, 5103, 5115, 5119, 5147, 5151, 5183, 5211, 5223, 5231, 5247, 5275, 5279, 5287
5311, 5343, 5351, 5359, 5375, 5403, 5423, 5447, 5479, 5503, 5535, 5567, 5595, 5599, 5615, 5631
5659, 5663, 5679, 5735, 5759, 5787, 5791, 5823, 5863, 5887, 5915, 5979, 5991, 6015, 6047, 6055
6079, 6127, 6139, 6143, 6171, 6175, 6191, 6207, 6235, 6247, 6255, 6271, 6299, 6303, 6311, 6367
6383, 6395, 6399, 6427, 6463, 6471, 6503, 6559, 6591, 6623, 6639, 6651, 6655, 6703, 6719, 6759
6767, 6783, 6811, 6823, 6847, 6887, 6895, 6907, 6911, 6939, 6975, 6983, 7003, 7015, 7039, 7071
7103, 7135, 7151, 7163, 7167, 7195, 7199, 7231, 7271, 7279, 7295, 7323, 7327, 7335, 7359, 7407
7419, 7423, 7451, 7471, 7483, 7487, 7495, 7527, 7551, 7583, 7615, 7647, 7663, 7679, 7707, 7711
7727, 7783, 7807, 7835, 7839, 7871, 7919, 7935, 7963, 8007, 8027, 8039, 8063, 8095, 8127, 8175
8187, 8191, 8219, 8223, 8239, 8255, 8263, 8283, 8295, 8303, 8319, 8351, 8359, 8415, 8431, 8443
8447, 8475, 8511, 8519, 8539, 8551, 8607, 8639, 8671, 8687, 8703, 8731, 8751, 8795, 8831, 8859
8863, 8871, 8895, 8935, 8943, 8955, 8959, 8987, 9023, 9031, 9051, 9063, 9087, 9119, 9151, 9183
9191, 9199, 9215, 9243, 9247, 9287, 9307, 9319, 9343, 9371, 9375, 9383, 9447, 9455, 9467, 9471
9499, 9535, 9543, 9575, 9599, 9631, 9663, 9695, 9711, 9727, 9755, 9775, 9831, 9855, 9883, 9887
9895, 9959, 9967, 9983, 10011, 10075, 10087, 10111, 10143, 10151, 10175, 10235, 10239, 10267, 10287, 10303
10311, 10331, 10343, 10351, 10367, 10399, 10407, 10479, 10491, 10495, 10559, 10567, 10599, 10607, 10655, 10687
10719, 10735, 10751, 10779, 10799, 10843, 10863, 10879, 10907, 10911, 10919, 10943, 10983, 10991, 11003, 11007
11035, 11071, 11079, 11111, 11135, 11175, 11199, 11231, 11247, 11263, 11291, 11295, 11311, 11355, 11367, 11375
11391, 11419, 11423, 11431, 11455, 11495, 11503, 11515, 11519, 11547, 11551, 11567, 11583, 11591, 11623, 11679
11711, 11743, 11759, 11775, 11803, 11807, 11823, 11903, 11931, 11935, 11967, 12007, 12015, 12031, 12059, 12123
12135, 12191, 12199, 12223, 12255, 12287, 12315, 12319, 12335, 12359, 12379, 12399, 12415, 12447, 12455, 12479
12511, 12527, 12539, 12543, 12571, 12591, 12607, 12615, 12647, 12703, 12735, 12767, 12783, 12799, 12827, 12847
12891, 12911, 12927, 12955, 12959, 12967, 12991, 13031, 13039, 13051, 13055, 13083, 13119, 13127, 13159, 13183
13247, 13279, 13311, 13339, 13343, 13383, 13403, 13415, 13423, 13439, 13471, 13479, 13503, 13535, 13543, 13551
13563, 13567, 13595, 13615, 13631, 13639, 13671, 13695, 13727, 13759, 13791, 13823, 13851, 13855, 13871, 13927
13951, 13983, 14015, 14023, 14055, 14063, 14075, 14079, 14107, 14143, 14183, 14207, 14247, 14271, 14331, 14335
14363, 14367, 14383, 14399, 14407, 14427, 14439, 14447, 14463, 14495, 14503, 14559, 14575, 14587, 14591, 14619
14655, 14663, 14695, 14783, 14815, 14831, 14847, 14895, 14939, 14951, 14959, 14975, 15003, 15007, 15015, 15039
15079, 15087, 15099, 15103, 15131, 15167, 15207, 15231, 15259, 15271, 15295, 15327, 15343, 15355, 15359, 15387
15391, 15423, 15431, 15451, 15463, 15471, 15487, 15515, 15519, 15527, 15551, 15591, 15599, 15611, 15615, 15643
15663, 15679, 15719, 15743, 15775, 15807, 15839, 15855, 15871, 15899, 15903, 15911, 15919, 15963, 15975, 15999
16027, 16031, 16063, 16103, 16111, 16127, 16155, 16219, 16231, 16255, 16287, 16295, 16319, 16367, 16379, 16383
### Nouveaux résidus couverts en passant de m = 13 à m = 14
Nombre : 104 (parmi les deux enfants modulo 2^14 des résidus non couverts au palier précédent).
255, 347, 539, 679, 999, 1191, 1563, 1703, 1983, 2075, 2095, 2415, 2587, 2607, 3039, 3119
3359, 3551, 4063, 4223, 4455, 4859, 4927, 5191, 5371, 5439, 5831, 5871, 5883, 5951, 6215, 6747
6815, 7067, 7079, 7239, 7259, 7399, 7719, 7771, 7911, 8103, 8383, 8423, 8495, 8775, 8815, 9127
9135, 9327, 9407, 9439, 9519, 9607, 9759, 9839, 9919, 10079, 10271, 10431, 10463, 10523, 10543, 10663
10783, 10855, 11023, 11259, 11327, 11487, 11647, 11879, 11899, 12079, 12159, 12271, 12283, 12351, 12391, 12671
12903, 13023, 13147, 13215, 13295, 13307, 13375, 13467, 13787, 13807, 13979, 14171, 14239, 14319, 14491, 14751
14843, 14911, 15175, 15195, 15263, 15675, 15687, 16199
Annotations (type, horizon, somme A, seuil N) pour les 24 premiers :
- r=255 : D ; horizon=8 ; A=13 ; N=4
- r=347 : D ; horizon=6 ; A=13 ; N=1
- r=539 : D ; horizon=8 ; A=13 ; N=7
- r=679 : D ; horizon=8 ; A=13 ; N=6
- r=999 : D ; horizon=6 ; A=13 ; N=1
- r=1191 : D ; horizon=8 ; A=13 ; N=6
- r=1563 : D ; horizon=8 ; A=13 ; N=6
- r=1703 : D ; horizon=7 ; A=13 ; N=1
- r=1983 : D ; horizon=8 ; A=13 ; N=5
- r=2075 : D ; horizon=8 ; A=13 ; N=6
- r=2095 : D ; horizon=8 ; A=13 ; N=6
- r=2415 : D ; horizon=6 ; A=13 ; N=1
- r=2587 : D ; horizon=7 ; A=13 ; N=1
- r=2607 : D ; horizon=8 ; A=13 ; N=6
- r=3039 : D ; horizon=8 ; A=13 ; N=6
- r=3119 : D ; horizon=7 ; A=13 ; N=1
- r=3359 : D ; horizon=6 ; A=13 ; N=1
- r=3551 : D ; horizon=8 ; A=13 ; N=5
- r=4063 : D ; horizon=7 ; A=13 ; N=1
- r=4223 : D ; horizon=8 ; A=13 ; N=4
- r=4455 : D ; horizon=8 ; A=13 ; N=5
- r=4859 : D ; horizon=8 ; A=13 ; N=8
- r=4927 : D ; horizon=8 ; A=13 ; N=5
- r=5191 : D ; horizon=8 ; A=13 ; N=8
### Palier m = 15 (mod 2^15 = 32768)
Nombre de résidus impairs non couverts : 1345 sur 16384.
27, 31, 47, 63, 71, 91, 103, 111, 127, 159, 167, 223, 239, 251, 283, 303
319, 327, 359, 415, 447, 479, 495, 511, 559, 583, 603, 623, 639, 667, 671, 703
743, 751, 763, 767, 795, 831, 839, 859, 871, 895, 927, 943, 959, 991, 1007, 1023
1051, 1055, 1095, 1115, 1127, 1151, 1179, 1183, 1247, 1255, 1263, 1275, 1279, 1307, 1327, 1343
1383, 1407, 1439, 1471, 1503, 1519, 1535, 1567, 1583, 1639, 1647, 1663, 1691, 1695, 1727, 1767
1775, 1791, 1819, 1883, 1887, 1895, 1919, 1951, 1959, 2043, 2047, 2111, 2119, 2139, 2151, 2159
2175, 2207, 2215, 2271, 2287, 2299, 2303, 2331, 2351, 2367, 2375, 2407, 2463, 2471, 2495, 2527
2543, 2559, 2591, 2651, 2671, 2687, 2715, 2719, 2727, 2751, 2791, 2799, 2811, 2831, 2843, 2879
2887, 2919, 2943, 2983, 3007, 3055, 3071, 3099, 3103, 3135, 3163, 3175, 3183, 3199, 3227, 3231
3263, 3295, 3303, 3311, 3323, 3327, 3355, 3375, 3391, 3399, 3431, 3455, 3487, 3519, 3567, 3583
3611, 3615, 3631, 3711, 3739, 3743, 3775, 3815, 3823, 3839, 3867, 3931, 3943, 3999, 4007, 4031
4079, 4095, 4127, 4159, 4167, 4187, 4199, 4207, 4255, 4263, 4287, 4319, 4335, 4347, 4351, 4379
4399, 4415, 4423, 4479, 4511, 4575, 4591, 4607, 4635, 4655, 4699, 4719, 4735, 4763, 4767, 4775
4799, 4839, 4847, 4863, 4891, 4935, 4967, 4991, 5023, 5055, 5103, 5119, 5147, 5151, 5183, 5211
5223, 5231, 5247, 5279, 5287, 5311, 5343, 5351, 5359, 5375, 5403, 5423, 5447, 5479, 5503, 5535
5567, 5599, 5631, 5659, 5663, 5679, 5735, 5759, 5787, 5791, 5823, 5863, 5887, 5915, 5991, 6015
6047, 6055, 6079, 6127, 6139, 6143, 6171, 6175, 6191, 6207, 6235, 6247, 6255, 6303, 6311, 6367
6383, 6395, 6399, 6427, 6463, 6471, 6503, 6591, 6623, 6639, 6651, 6655, 6703, 6759, 6767, 6783
6811, 6823, 6847, 6887, 6895, 6907, 6911, 6939, 7039, 7071, 7103, 7135, 7151, 7163, 7167, 7195
7199, 7231, 7271, 7279, 7295, 7323, 7327, 7335, 7359, 7407, 7423, 7451, 7471, 7487, 7495, 7527
7551, 7583, 7615, 7647, 7663, 7679, 7707, 7711, 7727, 7783, 7807, 7835, 7839, 7871, 7935, 7963
8027, 8039, 8063, 8095, 8127, 8175, 8187, 8191, 8219, 8223, 8239, 8255, 8283, 8295, 8303, 8319
8351, 8359, 8415, 8431, 8443, 8475, 8511, 8519, 8539, 8551, 8607, 8639, 8671, 8687, 8703, 8751
8795, 8831, 8859, 8895, 8935, 8943, 8955, 8959, 8987, 9023, 9031, 9051, 9063, 9087, 9119, 9151
9183, 9199, 9215, 9243, 9247, 9287, 9319, 9343, 9371, 9375, 9383, 9455, 9467, 9471, 9499, 9535
9543, 9575, 9599, 9631, 9663, 9695, 9711, 9727, 9775, 9831, 9855, 9883, 9887, 9959, 9967, 9983
10011, 10075, 10087, 10111, 10143, 10235, 10239, 10267, 10287, 10303, 10311, 10331, 10343, 10351, 10367, 10399
10407, 10479, 10491, 10495, 10559, 10567, 10599, 10607, 10655, 10687, 10719, 10735, 10751, 10843, 10863, 10879
10907, 10911, 10919, 10943, 10983, 10991, 11003, 11007, 11035, 11071, 11079, 11111, 11135, 11175, 11199, 11231
11247, 11263, 11291, 11295, 11311, 11355, 11367, 11391, 11419, 11423, 11431, 11495, 11503, 11515, 11519, 11547
11551, 11567, 11583, 11591, 11623, 11679, 11711, 11759, 11775, 11803, 11807, 11823, 11903, 11931, 11935, 11967
12007, 12015, 12031, 12059, 12123, 12135, 12191, 12199, 12223, 12255, 12287, 12315, 12335, 12359, 12379, 12399
12415, 12447, 12455, 12479, 12511, 12527, 12539, 12543, 12571, 12591, 12607, 12615, 12703, 12735, 12767, 12783
12799, 12827, 12847, 12891, 12911, 12927, 12955, 12959, 12967, 12991, 13031, 13039, 13055, 13119, 13127, 13159
13183, 13247, 13279, 13311, 13339, 13343, 13383, 13403, 13415, 13423, 13439, 13471, 13479, 13503, 13535, 13543
13551, 13563, 13567, 13595, 13615, 13639, 13671, 13695, 13727, 13759, 13791, 13823, 13851, 13855, 13871, 13951
13983, 14015, 14023, 14055, 14063, 14079, 14107, 14143, 14183, 14247, 14271, 14335, 14363, 14367, 14383, 14399
14407, 14427, 14439, 14447, 14463, 14495, 14503, 14559, 14575, 14587, 14591, 14619, 14655, 14663, 14695, 14783
14815, 14831, 14847, 14895, 14951, 14959, 14975, 15003, 15007, 15015, 15039, 15079, 15087, 15099, 15103, 15131
15167, 15207, 15231, 15271, 15295, 15327, 15343, 15355, 15359, 15387, 15391, 15423, 15431, 15451, 15463, 15471
15487, 15519, 15527, 15551, 15591, 15599, 15611, 15615, 15643, 15663, 15679, 15719, 15743, 15775, 15807, 15839
15871, 15899, 15903, 15911, 15919, 15975, 15999, 16027, 16031, 16063, 16111, 16127, 16155, 16231, 16255, 16287
16295, 16319, 16367, 16379, 16383, 16411, 16415, 16431, 16447, 16455, 16475, 16487, 16495, 16511, 16543, 16551
16575, 16607, 16615, 16623, 16635, 16667, 16703, 16711, 16743, 16831, 16863, 16879, 16895, 16943, 16987, 17023
17051, 17055, 17087, 17127, 17135, 17147, 17151, 17179, 17215, 17243, 17255, 17279, 17311, 17319, 17343, 17375
17391, 17407, 17435, 17439, 17479, 17499, 17511, 17519, 17535, 17563, 17567, 17599, 17639, 17647, 17659, 17663
17691, 17727, 17735, 17767, 17791, 17799, 17823, 17855, 17887, 17903, 17919, 17967, 18023, 18047, 18075, 18079
18151, 18159, 18175, 18203, 18267, 18279, 18303, 18335, 18343, 18427, 18431, 18463, 18495, 18503, 18523, 18535
18543, 18559, 18591, 18599, 18623, 18671, 18683, 18751, 18759, 18791, 18847, 18879, 18911, 18927, 18943, 19035
19047, 19055, 19071, 19099, 19103, 19135, 19175, 19183, 19195, 19199, 19227, 19263, 19271, 19303, 19327, 19367
19391, 19439, 19451, 19455, 19483, 19487, 19547, 19559, 19567, 19583, 19611, 19615, 19623, 19647, 19687, 19695
19707, 19711, 19739, 19759, 19775, 19783, 19815, 19871, 19903, 19951, 19967, 19999, 20015, 20071, 20091, 20095
20123, 20127, 20159, 20199, 20207, 20223, 20251, 20271, 20315, 20327, 20351, 20383, 20391, 20475, 20479, 20507
20511, 20527, 20551, 20571, 20591, 20639, 20647, 20671, 20703, 20719, 20731, 20735, 20763, 20783, 20799, 20807
20895, 20927, 20959, 20975, 20991, 21019, 21083, 21095, 21103, 21119, 21147, 21151, 21159, 21183, 21215, 21223
21231, 21247, 21275, 21319, 21339, 21351, 21375, 21439, 21471, 21499, 21503, 21531, 21535, 21595, 21607, 21615
21631, 21659, 21663, 21671, 21695, 21727, 21735, 21743, 21759, 21787, 21807, 21831, 21863, 21887, 21919, 21951
21979, 21999, 22015, 22043, 22047, 22063, 22119, 22143, 22175, 22207, 22247, 22271, 22299, 22363, 22375, 22399
22439, 22463, 22523, 22527, 22555, 22559, 22575, 22591, 22619, 22631, 22639, 22655, 22683, 22687, 22695, 22751
22767, 22779, 22783, 22811, 22847, 22855, 22943, 22975, 23007, 23023, 23039, 23087, 23103, 23143, 23151, 23195
23207, 23231, 23271, 23279, 23295, 23323, 23359, 23367, 23387, 23399, 23423, 23487, 23519, 23535, 23547, 23551
23579, 23583, 23615, 23655, 23663, 23679, 23707, 23711, 23719, 23743, 23791, 23803, 23807, 23835, 23855, 23867
23911, 23935, 23967, 23999, 24031, 24047, 24063, 24091, 24095, 24111, 24167, 24191, 24219, 24223, 24255, 24303
24319, 24347, 24391, 24411, 24423, 24447, 24479, 24511, 24559, 24571, 24575, 24603, 24607, 24623, 24639, 24647
24667, 24679, 24687, 24703, 24735, 24743, 24799, 24827, 24831, 24859, 24895, 24903, 24935, 24991, 25023, 25055
25071, 25087, 25115, 25135, 25215, 25243, 25247, 25255, 25279, 25319, 25327, 25339, 25343, 25371, 25407, 25415
25435, 25447, 25471, 25503, 25535, 25567, 25575, 25583, 25599, 25627, 25631, 25671, 25691, 25703, 25727, 25755
25831, 25839, 25851, 25855, 25883, 25919, 25927, 25959, 25983, 26015, 26047, 26079, 26095, 26111, 26139, 26159
26215, 26239, 26267, 26271, 26279, 26351, 26367, 26395, 26459, 26471, 26495, 26527, 26535, 26559, 26619, 26623
26687, 26695, 26715, 26727, 26735, 26751, 26783, 26791, 26863, 26875, 26879, 26943, 26951, 26983, 27039, 27071
27103, 27119, 27135, 27163, 27183, 27227, 27263, 27291, 27295, 27303, 27327, 27367, 27375, 27387, 27391, 27419
27455, 27463, 27495, 27519, 27559, 27583, 27631, 27647, 27675, 27679, 27739, 27751, 27759, 27775, 27803, 27807
27815, 27839, 27879, 27887, 27899, 27903, 27931, 27967, 27975, 28007, 28063, 28095, 28127, 28143, 28159, 28187
28207, 28287, 28315, 28319, 28391, 28399, 28415, 28443, 28507, 28519, 28575, 28583, 28607, 28671, 28699, 28703
28719, 28743, 28763, 28783, 28831, 28839, 28863, 28911, 28923, 28927, 28975, 28991, 28999, 29031, 29087, 29119
29151, 29167, 29183, 29211, 29231, 29275, 29295, 29311, 29339, 29343, 29351, 29375, 29415, 29423, 29435, 29439
29467, 29511, 29543, 29567, 29631, 29663, 29695, 29723, 29727, 29787, 29799, 29807, 29823, 29855, 29863, 29887
29919, 29927, 29935, 29951, 29979, 29999, 30015, 30023, 30055, 30111, 30143, 30175, 30207, 30235, 30239, 30255
30311, 30335, 30367, 30399, 30439, 30459, 30463, 30491, 30567, 30591, 30631, 30655, 30715, 30719, 30747, 30751
30767, 30811, 30831, 30847, 30879, 30887, 30943, 30959, 30971, 30975, 31003, 31039, 31047, 31079, 31167, 31199
31215, 31231, 31279, 31323, 31335, 31343, 31359, 31387, 31399, 31423, 31463, 31471, 31483, 31487, 31515, 31551
31591, 31615, 31643, 31679, 31711, 31739, 31743, 31771, 31775, 31807, 31847, 31855, 31871, 31899, 31903, 31911
31935, 31983, 31995, 31999, 32027, 32047, 32063, 32103, 32127, 32159, 32191, 32223, 32239, 32255, 32283, 32287
32303, 32347, 32359, 32383, 32415, 32447, 32487, 32495, 32511, 32539, 32603, 32615, 32639, 32703, 32751, 32763
32767
### Nouveaux résidus couverts en passant de m = 14 à m = 15
Nombre : 159 (parmi les deux enfants modulo 2^15 des résidus non couverts au palier précédent).
191, 231, 935, 1135, 1215, 1351, 1415, 2079, 2239, 2663, 2815, 3067, 3239, 3687, 3707, 3887
3967, 4091, 4123, 4143, 4543, 4711, 4831, 4955, 5087, 5115, 5275, 5595, 5615, 5979, 6271, 6299
6559, 6719, 6975, 6983, 7003, 7015, 7419, 7483, 7919, 8007, 8263, 8447, 8731, 8863, 8871, 9191
9307, 9447, 9755, 9895, 10151, 10175, 10779, 10799, 11375, 11455, 11743, 12319, 12647, 13051, 13083, 13631
13927, 14075, 14207, 14331, 14939, 15259, 15515, 15855, 15963, 16103, 16219, 16687, 16799, 16967, 17007, 17223
17327, 17631, 17711, 17951, 18031, 18111, 18271, 18655, 18687, 18715, 18735, 18855, 18975, 19111, 19215, 19519
19679, 19839, 19995, 20415, 20463, 20543, 20583, 20863, 21039, 21407, 21487, 21567, 21983, 22171, 22431, 22511
22887, 23035, 23167, 23291, 23455, 23871, 23879, 24815, 24923, 25179, 25759, 25767, 26343, 26651, 26671, 26991
27247, 27615, 27695, 27935, 27951, 28191, 28351, 28639, 28799, 28895, 28955, 29503, 29767, 29947, 30079, 30407
30447, 30527, 30783, 30791, 30823, 31391, 31655, 31727, 31815, 31835, 31975, 32295, 32411, 32671, 32679
Annotations (type, horizon, somme A, seuil N) pour les 24 premiers :
- r=191 : D ; horizon=8 ; A=14 ; N=1
- r=231 : D ; horizon=7 ; A=14 ; N=1
- r=935 : D ; horizon=7 ; A=14 ; N=1
- r=1135 : D ; horizon=8 ; A=14 ; N=1
- r=1215 : D ; horizon=8 ; A=14 ; N=1
- r=1351 : F ; horizon=9 ; A=14 ; N=5
- r=1415 : D ; horizon=4 ; A=14 ; N=1
- r=2079 : D ; horizon=8 ; A=14 ; N=1
- r=2239 : D ; horizon=7 ; A=14 ; N=1
- r=2663 : D ; horizon=8 ; A=14 ; N=1
- r=2815 : F ; horizon=9 ; A=14 ; N=3
- r=3067 : D ; horizon=8 ; A=14 ; N=2
- r=3239 : F ; horizon=9 ; A=14 ; N=5
- r=3687 : D ; horizon=8 ; A=14 ; N=1
- r=3707 : D ; horizon=5 ; A=14 ; N=1
- r=3887 : D ; horizon=6 ; A=14 ; N=1
- r=3967 : D ; horizon=8 ; A=14 ; N=1
- r=4091 : D ; horizon=8 ; A=14 ; N=2
- r=4123 : F ; horizon=9 ; A=14 ; N=5
- r=4143 : F ; horizon=9 ; A=14 ; N=5
- r=4543 : F ; horizon=9 ; A=14 ; N=3
- r=4711 : D ; horizon=7 ; A=14 ; N=1
- r=4831 : D ; horizon=6 ; A=14 ; N=1
- r=4955 : D ; horizon=8 ; A=14 ; N=2
### Palier m = 16 (mod 2^16 = 65536)
Nombre de résidus impairs non couverts : 2446 sur 32768.
27, 31, 47, 63, 71, 91, 103, 111, 159, 167, 223, 239, 251, 283, 319, 327
359, 415, 447, 479, 495, 511, 559, 603, 639, 667, 671, 703, 743, 751, 763, 767
795, 831, 859, 871, 895, 927, 959, 991, 1007, 1023, 1051, 1055, 1115, 1127, 1151, 1179
1183, 1247, 1255, 1263, 1279, 1307, 1327, 1343, 1383, 1407, 1439, 1471, 1503, 1519, 1535, 1567
1583, 1639, 1647, 1663, 1691, 1695, 1727, 1767, 1791, 1819, 1883, 1887, 1895, 1919, 1951, 1959
2043, 2047, 2111, 2119, 2139, 2151, 2159, 2175, 2207, 2215, 2287, 2299, 2303, 2367, 2375, 2407
2463, 2495, 2527, 2543, 2559, 2651, 2671, 2687, 2715, 2719, 2751, 2791, 2799, 2811, 2843, 2879
2887, 2919, 2943, 3007, 3055, 3071, 3099, 3103, 3135, 3175, 3183, 3199, 3227, 3231, 3263, 3295
3311, 3323, 3327, 3355, 3375, 3391, 3399, 3431, 3455, 3487, 3519, 3567, 3583, 3611, 3615, 3631
3711, 3739, 3775, 3815, 3823, 3839, 3867, 3931, 3943, 3999, 4007, 4031, 4095, 4127, 4167, 4187
4207, 4255, 4263, 4287, 4319, 4335, 4347, 4351, 4379, 4399, 4415, 4423, 4511, 4575, 4591, 4607
4635, 4699, 4719, 4735, 4763, 4767, 4775, 4799, 4839, 4847, 4863, 4891, 4935, 4967, 4991, 5023
5055, 5103, 5119, 5147, 5151, 5183, 5211, 5223, 5247, 5279, 5287, 5343, 5351, 5359, 5375, 5403
5423, 5447, 5479, 5503, 5535, 5567, 5599, 5659, 5663, 5679, 5735, 5759, 5791, 5823, 5863, 5887
5915, 5991, 6015, 6055, 6079, 6139, 6143, 6171, 6175, 6191, 6207, 6235, 6247, 6255, 6303, 6311
6367, 6383, 6395, 6399, 6427, 6463, 6471, 6591, 6623, 6639, 6651, 6655, 6703, 6767, 6811, 6823
6847, 6887, 6895, 6907, 6911, 6939, 7039, 7071, 7103, 7135, 7151, 7163, 7167, 7195, 7231, 7271
7279, 7295, 7323, 7327, 7335, 7359, 7407, 7423, 7451, 7471, 7487, 7527, 7551, 7583, 7615, 7647
7663, 7679, 7707, 7711, 7727, 7783, 7807, 7835, 7839, 7871, 7935, 7963, 8027, 8039, 8063, 8095
8127, 8175, 8191, 8219, 8223, 8239, 8255, 8283, 8295, 8303, 8319, 8351, 8359, 8415, 8443, 8475
8511, 8519, 8539, 8551, 8607, 8639, 8671, 8687, 8703, 8751, 8795, 8831, 8859, 8895, 8935, 8943
8955, 8959, 8987, 9023, 9031, 9051, 9063, 9119, 9151, 9183, 9199, 9215, 9243, 9247, 9287, 9319
9343, 9371, 9375, 9455, 9467, 9471, 9499, 9535, 9543, 9575, 9599, 9631, 9663, 9695, 9711, 9727
9775, 9831, 9855, 9883, 9887, 9967, 9983, 10011, 10087, 10111, 10143, 10235, 10239, 10267, 10287, 10303
10311, 10331, 10343, 10351, 10367, 10399, 10407, 10479, 10491, 10495, 10559, 10567, 10599, 10607, 10687, 10719
10751, 10843, 10863, 10879, 10907, 10911, 10919, 10943, 10983, 10991, 11003, 11007, 11035, 11071, 11079, 11111
11135, 11175, 11199, 11247, 11263, 11291, 11295, 11355, 11367, 11391, 11419, 11423, 11431, 11495, 11503, 11515
11519, 11547, 11583, 11591, 11623, 11679, 11711, 11759, 11775, 11803, 11823, 11903, 11931, 11935, 12007, 12015
12031, 12059, 12123, 12135, 12191, 12199, 12223, 12255, 12287, 12315, 12335, 12359, 12379, 12399, 12415, 12447
12455, 12479, 12511, 12527, 12539, 12571, 12591, 12607, 12615, 12703, 12735, 12767, 12783, 12799, 12827, 12847
12891, 12911, 12927, 12955, 12959, 12967, 12991, 13031, 13039, 13055, 13127, 13159, 13183, 13247, 13279, 13311
13339, 13343, 13383, 13403, 13415, 13423, 13439, 13471, 13479, 13503, 13535, 13543, 13551, 13563, 13567, 13595
13615, 13639, 13671, 13727, 13759, 13791, 13823, 13855, 13871, 13951, 13983, 14015, 14023, 14055, 14063, 14079
14107, 14143, 14183, 14247, 14335, 14363, 14367, 14383, 14399, 14427, 14439, 14447, 14463, 14495, 14503, 14559
14575, 14587, 14591, 14619, 14655, 14663, 14695, 14783, 14815, 14831, 14847, 14895, 14951, 14959, 14975, 15003
15015, 15039, 15079, 15087, 15099, 15103, 15131, 15167, 15207, 15231, 15271, 15295, 15327, 15355, 15359, 15387
15391, 15423, 15431, 15451, 15463, 15471, 15487, 15519, 15527, 15551, 15591, 15599, 15611, 15615, 15643, 15663
15679, 15719, 15743, 15775, 15807, 15871, 15899, 15903, 15911, 15975, 15999, 16027, 16031, 16063, 16111, 16127
16155, 16231, 16255, 16287, 16319, 16367, 16379, 16383, 16411, 16415, 16431, 16447, 16455, 16475, 16487, 16495
16511, 16543, 16551, 16607, 16623, 16635, 16667, 16703, 16711, 16743, 16831, 16863, 16879, 16895, 16943, 16987
17023, 17051, 17055, 17087, 17127, 17135, 17151, 17179, 17215, 17243, 17255, 17279, 17311, 17319, 17343, 17375
17391, 17407, 17435, 17439, 17479, 17499, 17511, 17519, 17535, 17563, 17567, 17599, 17639, 17647, 17659, 17663
17691, 17735, 17791, 17799, 17823, 17855, 17887, 17903, 17919, 17967, 18023, 18047, 18075, 18079, 18151, 18159
18175, 18203, 18267, 18279, 18303, 18335, 18343, 18427, 18431, 18495, 18503, 18523, 18535, 18543, 18559, 18591
18599, 18671, 18683, 18751, 18759, 18791, 18847, 18879, 18911, 18927, 18943, 19047, 19055, 19071, 19099, 19103
19135, 19175, 19183, 19195, 19227, 19263, 19271, 19303, 19327, 19367, 19391, 19439, 19455, 19483, 19487, 19547
19559, 19567, 19583, 19611, 19615, 19623, 19647, 19687, 19695, 19707, 19711, 19739, 19759, 19775, 19783, 19815
19871, 19903, 19951, 19967, 19999, 20015, 20095, 20123, 20127, 20159, 20199, 20207, 20223, 20251, 20315, 20327
20383, 20391, 20475, 20479, 20511, 20551, 20571, 20591, 20639, 20647, 20671, 20703, 20719, 20731, 20735, 20763
20799, 20807, 20895, 20959, 20975, 20991, 21019, 21083, 21095, 21119, 21147, 21151, 21159, 21183, 21215, 21231
21247, 21275, 21319, 21351, 21375, 21439, 21471, 21503, 21531, 21535, 21595, 21607, 21615, 21631, 21663, 21671
21695, 21727, 21735, 21743, 21759, 21787, 21807, 21831, 21863, 21887, 21919, 21951, 22015, 22043, 22047, 22063
22119, 22143, 22175, 22207, 22247, 22271, 22299, 22363, 22375, 22399, 22439, 22463, 22523, 22527, 22555, 22559
22575, 22591, 22619, 22631, 22639, 22683, 22687, 22695, 22767, 22779, 22783, 22847, 22855, 22943, 22975, 23007
23023, 23039, 23087, 23103, 23143, 23151, 23195, 23207, 23271, 23279, 23295, 23323, 23359, 23399, 23423, 23487
23519, 23535, 23547, 23551, 23579, 23583, 23615, 23655, 23663, 23679, 23707, 23711, 23719, 23743, 23791, 23807
23835, 23855, 23911, 23935, 23967, 23999, 24031, 24047, 24063, 24091, 24095, 24111, 24167, 24191, 24219, 24223
24255, 24319, 24347, 24391, 24411, 24423, 24447, 24479, 24511, 24571, 24575, 24603, 24607, 24623, 24647, 24667
24687, 24703, 24735, 24743, 24799, 24827, 24831, 24859, 24895, 24903, 24935, 24991, 25023, 25055, 25071, 25087
25135, 25215, 25243, 25247, 25279, 25319, 25327, 25339, 25343, 25371, 25407, 25415, 25435, 25447, 25471, 25503
25535, 25567, 25583, 25599, 25627, 25631, 25671, 25703, 25727, 25755, 25839, 25851, 25855, 25883, 25919, 25927
25959, 25983, 26015, 26047, 26079, 26095, 26111, 26139, 26159, 26215, 26239, 26271, 26279, 26351, 26367, 26395
26459, 26471, 26495, 26535, 26559, 26619, 26623, 26687, 26695, 26715, 26727, 26735, 26751, 26783, 26791, 26863
26875, 26879, 26943, 26951, 26983, 27039, 27071, 27103, 27119, 27135, 27227, 27263, 27291, 27295, 27303, 27327
27367, 27375, 27387, 27391, 27419, 27455, 27463, 27495, 27519, 27559, 27583, 27631, 27647, 27675, 27679, 27739
27751, 27775, 27803, 27807, 27815, 27879, 27887, 27899, 27903, 27931, 27967, 28007, 28063, 28095, 28127, 28143
28159, 28187, 28207, 28287, 28315, 28319, 28391, 28399, 28415, 28443, 28507, 28519, 28575, 28583, 28607, 28671
28699, 28703, 28719, 28743, 28763, 28783, 28831, 28839, 28863, 28911, 28923, 28927, 28975, 28991, 28999, 29087
29119, 29151, 29167, 29183, 29211, 29231, 29275, 29295, 29311, 29339, 29343, 29351, 29375, 29415, 29423, 29435
29439, 29511, 29543, 29567, 29631, 29663, 29695, 29723, 29727, 29787, 29799, 29807, 29823, 29855, 29887, 29919
29927, 29935, 29951, 29979, 29999, 30015, 30023, 30055, 30111, 30143, 30175, 30207, 30235, 30239, 30255, 30311
30335, 30367, 30399, 30439, 30463, 30491, 30567, 30591, 30631, 30655, 30719, 30747, 30751, 30767, 30811, 30831
30847, 30879, 30887, 30943, 30959, 30971, 30975, 31003, 31039, 31047, 31079, 31167, 31199, 31215, 31231, 31279
31323, 31335, 31343, 31359, 31387, 31399, 31423, 31463, 31471, 31483, 31487, 31515, 31551, 31591, 31615, 31643
31679, 31739, 31743, 31775, 31807, 31847, 31855, 31871, 31899, 31903, 31911, 31935, 31983, 31995, 31999, 32027
32047, 32063, 32103, 32127, 32159, 32191, 32223, 32239, 32255, 32283, 32287, 32303, 32359, 32383, 32415, 32447
32495, 32511, 32539, 32615, 32639, 32703, 32751, 32763, 32767, 32795, 32799, 32815, 32831, 32839, 32859, 32871
32879, 32895, 32927, 32935, 32991, 33007, 33019, 33051, 33071, 33087, 33095, 33127, 33215, 33247, 33263, 33279
33327, 33351, 33371, 33391, 33407, 33435, 33439, 33471, 33511, 33519, 33531, 33535, 33563, 33607, 33627, 33639
33663, 33695, 33711, 33727, 33759, 33775, 33791, 33819, 33823, 33863, 33883, 33895, 33947, 33951, 34023, 34031
34043, 34047, 34075, 34111, 34151, 34175, 34207, 34239, 34271, 34287, 34303, 34351, 34407, 34431, 34459, 34463
34535, 34543, 34559, 34587, 34651, 34663, 34687, 34719, 34727, 34811, 34815, 34879, 34907, 34919, 34927, 34943
34975, 34983, 35039, 35055, 35099, 35119, 35135, 35143, 35175, 35231, 35239, 35263, 35295, 35311, 35327, 35359
35419, 35439, 35455, 35483, 35495, 35519, 35559, 35579, 35599, 35611, 35647, 35655, 35687, 35711, 35751, 35775
35823, 35839, 35867, 35871, 35931, 35943, 35951, 35967, 35995, 35999, 36031, 36071, 36079, 36091, 36095, 36123
36143, 36159, 36167, 36199, 36255, 36287, 36335, 36351, 36383, 36399, 36479, 36507, 36511, 36543, 36583, 36591
36607, 36635, 36699, 36711, 36767, 36847, 36863, 36895, 36927, 36935, 36967, 36975, 37023, 37031, 37087, 37103
37115, 37119, 37147, 37167, 37183, 37191, 37247, 37279, 37343, 37359, 37375, 37403, 37423, 37467, 37487, 37503
37531, 37535, 37543, 37567, 37607, 37615, 37631, 37659, 37703, 37735, 37759, 37823, 37887, 37915, 37919, 37979
37991, 37999, 38015, 38047, 38055, 38079, 38111, 38119, 38127, 38143, 38171, 38191, 38215, 38247, 38271, 38303
38335, 38399, 38427, 38431, 38447, 38503, 38527, 38555, 38559, 38591, 38631, 38655, 38683, 38759, 38783, 38815
38823, 38847, 38895, 38907, 38911, 38939, 38959, 38975, 39003, 39015, 39071, 39079, 39135, 39151, 39163, 39167
39195, 39231, 39239, 39271, 39359, 39391, 39407, 39423, 39471, 39527, 39535, 39551, 39579, 39591, 39615, 39655
39663, 39679, 39707, 39807, 39871, 39903, 39919, 39935, 39963, 39967, 39999, 40039, 40047, 40063, 40091, 40095
40103, 40127, 40175, 40191, 40219, 40239, 40263, 40295, 40319, 40351, 40383, 40415, 40431, 40447, 40475, 40479
40495, 40575, 40603, 40607, 40639, 40703, 40731, 40795, 40807, 40863, 40895, 40943, 40955, 40959, 40987, 40991
41007, 41023, 41051, 41063, 41071, 41087, 41119, 41127, 41183, 41199, 41211, 41243, 41279, 41287, 41319, 41375
41407, 41439, 41455, 41471, 41519, 41599, 41627, 41663, 41703, 41711, 41723, 41727, 41755, 41791, 41799, 41831
41855, 41887, 41919, 41951, 41967, 41983, 42011, 42015, 42055, 42087, 42111, 42151, 42223, 42235, 42239, 42267
42303, 42311, 42343, 42367, 42399, 42431, 42463, 42495, 42543, 42599, 42623, 42651, 42655, 42727, 42735, 42751
42779, 42843, 42855, 42879, 42911, 43003, 43007, 43071, 43079, 43099, 43111, 43119, 43135, 43167, 43175, 43247
43259, 43263, 43327, 43335, 43367, 43423, 43455, 43487, 43503, 43519, 43611, 43647, 43675, 43679, 43687, 43711
43751, 43759, 43771, 43775, 43803, 43839, 43879, 43903, 43943, 43967, 43999, 44015, 44031, 44059, 44063, 44079
44123, 44135, 44159, 44187, 44191, 44199, 44263, 44271, 44283, 44287, 44315, 44319, 44335, 44351, 44359, 44391
44479, 44527, 44543, 44571, 44575, 44591, 44671, 44699, 44703, 44735, 44775, 44783, 44799, 44827, 44891, 44903
44959, 44967, 44991, 45055, 45083, 45103, 45127, 45147, 45167, 45215, 45223, 45247, 45295, 45307, 45311, 45359
45375, 45383, 45471, 45503, 45535, 45551, 45567, 45615, 45659, 45679, 45695, 45723, 45727, 45759, 45799, 45807
45823, 45887, 45895, 45927, 45951, 46015, 46047, 46079, 46107, 46111, 46171, 46183, 46191, 46207, 46239, 46247
46271, 46303, 46311, 46319, 46363, 46383, 46407, 46439, 46463, 46495, 46527, 46559, 46591, 46619, 46623, 46639
46719, 46751, 46783, 46823, 46847, 46875, 46951, 47015, 47039, 47103, 47131, 47135, 47151, 47175, 47195, 47215
47231, 47263, 47271, 47327, 47343, 47355, 47359, 47387, 47423, 47431, 47463, 47551, 47583, 47599, 47615, 47719
47727, 47743, 47771, 47775, 47783, 47807, 47847, 47855, 47867, 47871, 47899, 47935, 47975, 47999, 48095, 48111
48123, 48127, 48155, 48159, 48191, 48231, 48239, 48255, 48287, 48295, 48319, 48367, 48379, 48383, 48411, 48431
48447, 48487, 48511, 48543, 48575, 48607, 48639, 48667, 48671, 48687, 48743, 48767, 48799, 48831, 48879, 48895
48923, 48999, 49023, 49063, 49087, 49135, 49147, 49151, 49179, 49183, 49199, 49215, 49223, 49243, 49255, 49263
49279, 49311, 49319, 49343, 49375, 49383, 49391, 49403, 49435, 49471, 49479, 49599, 49647, 49663, 49711, 49755
49791, 49819, 49823, 49855, 49895, 49903, 49915, 49919, 49947, 49983, 50011, 50023, 50047, 50079, 50111, 50143
50159, 50175, 50203, 50207, 50247, 50267, 50279, 50303, 50331, 50335, 50407, 50415, 50427, 50431, 50459, 50495
50535, 50559, 50591, 50623, 50655, 50671, 50687, 50735, 50791, 50815, 50843, 50847, 50919, 50927, 50943, 50971
51035, 51047, 51071, 51103, 51111, 51195, 51199, 51231, 51263, 51271, 51291, 51303, 51311, 51327, 51359, 51367
51391, 51439, 51451, 51527, 51559, 51615, 51647, 51679, 51695, 51711, 51803, 51823, 51839, 51867, 51871, 51903
51943, 51951, 51963, 51967, 51995, 52031, 52039, 52071, 52095, 52135, 52159, 52207, 52219, 52223, 52251, 52255
52315, 52327, 52335, 52351, 52379, 52383, 52415, 52455, 52463, 52475, 52479, 52507, 52527, 52543, 52551, 52583
52639, 52671, 52719, 52735, 52767, 52783, 52839, 52859, 52863, 52891, 52895, 52927, 52975, 52991, 53019, 53039
53083, 53095, 53119, 53151, 53159, 53247, 53275, 53279, 53295, 53319, 53339, 53359, 53407, 53415, 53439, 53471
53487, 53499, 53503, 53531, 53551, 53567, 53575, 53663, 53695, 53727, 53743, 53759, 53787, 53851, 53871, 53887
53915, 53919, 53927, 53951, 53991, 53999, 54015, 54043, 54087, 54107, 54119, 54143, 54207, 54267, 54271, 54299
54303, 54363, 54375, 54383, 54399, 54427, 54431, 54439, 54463, 54503, 54511, 54527, 54555, 54599, 54631, 54655
54687, 54719, 54747, 54767, 54783, 54811, 54831, 54887, 54911, 54943, 55015, 55039, 55067, 55143, 55167, 55207
55231, 55291, 55295, 55323, 55327, 55343, 55359, 55387, 55399, 55407, 55423, 55455, 55463, 55519, 55535, 55547
55551, 55579, 55615, 55623, 55743, 55775, 55791, 55807, 55855, 55911, 55919, 55963, 55975, 55999, 56039, 56047
56063, 56091, 56135, 56155, 56191, 56255, 56287, 56303, 56315, 56319, 56347, 56351, 56423, 56431, 56447, 56475
56479, 56487, 56511, 56559, 56571, 56575, 56623, 56635, 56679, 56735, 56767, 56799, 56815, 56831, 56859, 56863
56879, 56935, 56959, 56987, 56991, 57023, 57071, 57087, 57115, 57179, 57191, 57215, 57247, 57279, 57327, 57339
57343, 57371, 57375, 57391, 57407, 57435, 57447, 57455, 57471, 57503, 57511, 57567, 57595, 57627, 57663, 57671
57703, 57759, 57791, 57823, 57839, 57855, 57883, 57903, 57983, 58011, 58023, 58047, 58087, 58095, 58107, 58111
58139, 58175, 58183, 58203, 58215, 58239, 58303, 58335, 58343, 58367, 58395, 58399, 58439, 58459, 58495, 58523
58599, 58607, 58619, 58623, 58651, 58687, 58695, 58727, 58751, 58783, 58815, 58847, 58863, 58879, 58927, 58983
59007, 59035, 59039, 59119, 59135, 59163, 59227, 59239, 59263, 59295, 59387, 59391, 59455, 59463, 59483, 59495
59503, 59519, 59551, 59559, 59631, 59643, 59647, 59711, 59719, 59751, 59807, 59839, 59871, 59887, 59903, 59931
59951, 59995, 60031, 60063, 60071, 60095, 60135, 60143, 60155, 60159, 60187, 60223, 60231, 60263, 60287, 60327
60351, 60399, 60415, 60443, 60447, 60507, 60519, 60527, 60543, 60571, 60575, 60583, 60607, 60647, 60655, 60667
60671, 60699, 60735, 60743, 60775, 60831, 60863, 60911, 60927, 60955, 60975, 61055, 61083, 61087, 61159, 61167
61183, 61211, 61275, 61287, 61343, 61351, 61375, 61439, 61467, 61487, 61511, 61531, 61551, 61599, 61607, 61631
61679, 61691, 61695, 61743, 61759, 61799, 61855, 61887, 61919, 61935, 61951, 61979, 61999, 62043, 62063, 62079
62107, 62111, 62119, 62143, 62183, 62191, 62207, 62235, 62279, 62311, 62335, 62399, 62431, 62463, 62491, 62495
62555, 62567, 62575, 62591, 62623, 62631, 62655, 62687, 62695, 62703, 62719, 62747, 62767, 62791, 62823, 62879
62911, 62943, 62975, 63003, 63007, 63023, 63103, 63135, 63167, 63207, 63227, 63231, 63259, 63335, 63399, 63423
63483, 63487, 63519, 63579, 63599, 63615, 63647, 63711, 63727, 63739, 63743, 63771, 63807, 63815, 63847, 63935
63967, 63983, 63999, 64047, 64103, 64111, 64127, 64155, 64167, 64191, 64231, 64239, 64251, 64255, 64283, 64319
64359, 64383, 64447, 64479, 64507, 64511, 64539, 64543, 64575, 64615, 64623, 64639, 64671, 64679, 64703, 64751
64763, 64767, 64795, 64815, 64831, 64871, 64895, 64927, 64959, 64991, 65023, 65051, 65055, 65071, 65115, 65127
65151, 65183, 65215, 65255, 65263, 65279, 65307, 65371, 65383, 65407, 65471, 65519, 65531, 65535
### Nouveaux résidus couverts en passant de m = 15 à m = 16
Nombre : 244 (parmi les deux enfants modulo 2^16 des résidus non couverts au palier précédent).
127, 303, 583, 623, 839, 943, 1095, 1275, 1775, 2271, 2331, 2351, 2471, 2591, 2727, 2831
2983, 3163, 3303, 3743, 4079, 4159, 4199, 4479, 4655, 5231, 5311, 5631, 5787, 6047, 6127, 6503
6759, 6783, 7199, 7495, 8187, 8431, 9087, 9383, 9959, 10075, 10655, 10735, 11231, 11311, 11551, 11567
11807, 11967, 12543, 13119, 13695, 13851, 14271, 14407, 15007, 15343, 15839, 15919, 16295, 16575, 16615, 17147
17727, 17767, 18463, 18623, 19035, 19199, 19451, 20071, 20091, 20271, 20351, 20507, 20527, 20783, 20927, 21103
21223, 21339, 21499, 21659, 21979, 21999, 22655, 22751, 22811, 23231, 23367, 23387, 23803, 23867, 24303, 24559
24639, 24679, 25115, 25255, 25575, 25691, 25831, 26267, 26527, 27163, 27183, 27759, 27839, 27975, 29031, 29467
29863, 30459, 30715, 31711, 31771, 32347, 32487, 32603, 33183, 33599, 33919, 34015, 34095, 34335, 34415, 34495
34655, 34887, 35067, 35071, 35487, 35567, 35903, 36063, 36223, 36379, 36775, 36799, 36955, 37055, 37791, 37871
37951, 38367, 38943, 39023, 39419, 39675, 39839, 39931, 40255, 40551, 40831, 41307, 41563, 41819, 42139, 42143
42479, 43035, 43055, 43375, 43631, 43847, 44447, 45023, 45183, 45279, 45339, 45595, 45735, 46151, 46331, 46335
46791, 46831, 46911, 47167, 47207, 47663, 48039, 48063, 48199, 48219, 48359, 48679, 48795, 49055, 49511, 49631
50087, 50287, 50367, 50503, 50567, 51519, 51815, 52391, 52967, 53243, 53863, 53983, 54239, 54495, 54575, 54815
54975, 55131, 55451, 55711, 55871, 56127, 56167, 56383, 56603, 56703, 57159, 57415, 57599, 58015, 58271, 58351
58471, 58907, 59047, 59303, 59327, 60059, 60895, 61471, 61767, 62203, 62783, 63079, 63359, 63515, 63535, 63655
64091, 64411, 64667, 65007
Annotations (type, horizon, somme A, seuil N) pour les 24 premiers :
- r=127 : D ; horizon=9 ; A=15 ; N=2
- r=303 : D ; horizon=8 ; A=15 ; N=1
- r=583 : D ; horizon=6 ; A=15 ; N=1
- r=623 : D ; horizon=8 ; A=15 ; N=1
- r=839 : D ; horizon=9 ; A=15 ; N=3
- r=943 : D ; horizon=5 ; A=15 ; N=1
- r=1095 : D ; horizon=9 ; A=15 ; N=4
- r=1275 : D ; horizon=9 ; A=15 ; N=3
- r=1775 : D ; horizon=9 ; A=15 ; N=2
- r=2271 : D ; horizon=8 ; A=15 ; N=1
- r=2331 : D ; horizon=8 ; A=15 ; N=1
- r=2351 : D ; horizon=7 ; A=15 ; N=1
- r=2471 : D ; horizon=6 ; A=15 ; N=1
- r=2591 : D ; horizon=7 ; A=15 ; N=1
- r=2727 : D ; horizon=9 ; A=15 ; N=3
- r=2831 : D ; horizon=4 ; A=15 ; N=1
- r=2983 : D ; horizon=9 ; A=15 ; N=3
- r=3163 : D ; horizon=9 ; A=15 ; N=3
- r=3303 : D ; horizon=9 ; A=15 ; N=3
- r=3743 : D ; horizon=9 ; A=15 ; N=2
- r=4079 : D ; horizon=8 ; A=15 ; N=1
- r=4159 : D ; horizon=8 ; A=15 ; N=1
- r=4199 : D ; horizon=8 ; A=15 ; N=1
- r=4479 : D ; horizon=7 ; A=15 ; N=1