Files
zeekay b832ba2c39 Initial Torus commit
Forked from upstream concrete (BSD-3-Clause-Clear, © 2024 ZAMA) at HEAD
ecb729bb. Modifications copyright © 2026 Lux Industries Inc.

Rebranding scope:
  - Python module concrete → torus (across frontends/torus-python)
  - Rust module concrete-* → torus-* (across frontends/torus-rust)
  - MLIR dialect concretelang → toruslang (across compilers/torus-compiler)
  - Compiler optimizer concrete-optimizer → torus-optimizer
  - Backend concrete-cpu / concrete-cuda → torus-cpu / torus-cuda
  - Wire protocol concrete-protocol → torus-protocol
  - Parameter-curves concrete-security-curves-* → torus-security-curves-*
  - Public symbols concretelib → toruslib, ConcreteLang → TorusLang
  - URLs github.com/zama-ai/concrete → github.com/luxfhe/torus
  - URLs docs.zama.ai/concrete → docs.luxfhe.com/torus

Legal compliance:
  - LICENSE.txt retains original Copyright © 2024 ZAMA verbatim (§1-§2)
  - LICENSE.txt adds modifications copyright © 2026 Lux Industries Inc.
  - §3 endorsement clause: Torus is marketed exclusively as a Lux product;
    no Zama name used in README, docs, or marketing
  - NOTICE file provides factual attribution per legal best practice
    (not endorsement; required by upstream BSD-3-Clause-Clear)

README + NOTICE rewritten from scratch with Lux brand:
  - Quick-start in Python (torus.fhe)
  - Architecture diagram showing the gen-1 vtbl integration path
    (luxcpp/gpu → lux-private/gpu-kernels for CUDA/Metal/WebGPU)
  - Scheme coverage table: TFHE (luxfi/fhe), CKKS/BGV/BFV (luxfi/lattice)
  - Lux FHE family table: Torus / TorusVM / TorusEVM / TorusML / TorusNet

Known limitations (phase-2A scope):
  - PyPI package torus-fhe not yet published; the torus Python module
    is renamed structurally but pip-installable distribution is a
    follow-up (Phase 2A.1)
  - MLIR dialect rename is text-level; the compiler-internal LLVM
    rebuild (concrete-compiler-internal-llvm-project submodule) is
    structural and works; tablegen files renamed concrete→torus but the
    generated .inc files in the source tree will regenerate at build
    time
  - backends/torus-cuda/implementation/ is an upstream submodule
    pointer to the tfhe-rs source (not fetched in the staging clone);
    the CUDA backend body is delivered out-of-tree
  - ~100 test-fixture variable names like concrete_encoded_sample
    retain "concrete" as a math term (vs symbolic); these are inside
    tests/, not the public API; cleanup is a follow-up commit
  - 295 Python `from concrete import ...` residuals in luxfhe/ml-sdk
    consumer remain; that repo's import update is Phase 2B

This commit is the seed for the luxfhe/torus repo. Push as the first
commit to a fresh GitHub repo; do not re-import upstream Zama git
history.
2026-05-29 14:16:47 -07:00

270 lines
15 KiB
Plaintext

security level: 256
target p_error: 6.3e-5
per precision and log norm2:
- 1: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 5, 9, 1165, 1, 16, 3, 3, 115, 6.2e-5
- 1 : 5, 9, 1173, 1, 16, 3, 3, 116, 5.9e-5
- 2 : 5, 9, 1289, 1, 16, 2, 5, 120, 6.2e-5
- 3 : 6, 9, 1182, 1, 20, 3, 3, 141, 5.9e-5
- 4 : 6, 9, 1185, 1, 20, 3, 3, 142, 6.1e-5
- 5 : 6, 9, 1202, 1, 20, 3, 3, 144, 6.1e-5
- 6 : 6, 9, 1272, 1, 20, 3, 4, 151, 6.1e-5
- 7 : 5, 9, 1124, 2, 11, 5, 2, 175, 6.2e-5
- 8 : 4, 10, 1292, 1, 23, 2, 5, 206, 6.3e-5
- 9 : 6, 9, 1181, 2, 13, 3, 3, 210, 6.3e-5
- 10: 6, 9, 1184, 2, 13, 3, 3, 210, 6.0e-5
- 11: 6, 9, 1195, 2, 13, 3, 3, 212, 6.2e-5
- 12: 6, 9, 1149, 2, 13, 5, 2, 218, 6.1e-5
- 13: 6, 9, 1113, 3, 10, 5, 2, 276, 5.7e-5
- 14: 6, 9, 1116, 3, 10, 5, 2, 277, 6.2e-5
- 15: 6, 9, 1134, 3, 10, 5, 2, 281, 6.2e-5
- 16: 4, 10, 1208, 2, 15, 4, 3, 307, 6.1e-5
- 17: 6, 9, 1143, 4, 8, 5, 2, 350, 5.9e-5
- 18: 4, 10, 1129, 3, 12, 5, 2, 385, 6.0e-5
- 19: 4, 10, 1139, 3, 12, 5, 2, 388, 5.7e-5
- 20: 4, 10, 1254, 3, 12, 4, 3, 416, 6.2e-5
- 21: 4, 10, 1136, 4, 9, 5, 2, 476, 6.2e-5
- 22: 4, 10, 1177, 4, 9, 6, 2, 502, 6.1e-5
- 23: 4, 10, 1149, 5, 8, 5, 2, 571, 5.9e-5
- 24: 4, 10, 1154, 6, 7, 5, 2, 664, 6.2e-5
- 25: 4, 10, 1162, 7, 6, 5, 2, 759, 6.1e-5
- 26: 4, 10, 1166, 9, 5, 6, 2, 953, 6.1e-5
- 27: 4, 10, 1184, 11, 4, 6, 2, 1152, 6.2e-5
- 28: 4, 10, 1190, 21, 2, 6, 2, 2088, 6.2e-5
- 29: 4, 10, 1181, 44, 1, 12, 1, 4249, 6.2e-5
# no solution starting from log norm2 = 30
- 2: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 5, 9, 1289, 1, 16, 3, 4, 127, 5.7e-5
- 1 : 5, 9, 1322, 1, 16, 3, 4, 130, 6.1e-5
- 2 : 6, 9, 1291, 1, 20, 3, 4, 153, 6.3e-5
- 3 : 6, 9, 1294, 1, 20, 3, 4, 154, 5.7e-5
- 4 : 6, 9, 1303, 1, 20, 3, 4, 155, 6.3e-5
- 5 : 3, 10, 1308, 1, 20, 4, 3, 175, 6.2e-5
- 6 : 5, 9, 1258, 2, 11, 4, 3, 189, 6.3e-5
- 7 : 4, 10, 1307, 1, 23, 3, 4, 218, 5.8e-5
- 8 : 6, 9, 1238, 2, 13, 4, 3, 227, 5.6e-5
- 9 : 6, 9, 1239, 2, 13, 4, 3, 227, 6.0e-5
- 10: 6, 9, 1246, 2, 13, 4, 3, 228, 5.7e-5
- 11: 6, 9, 1289, 2, 13, 4, 3, 236, 6.3e-5
- 12: 6, 9, 1238, 3, 10, 4, 3, 299, 6.3e-5
- 13: 6, 9, 1243, 3, 10, 4, 3, 300, 5.9e-5
- 14: 6, 9, 1266, 3, 10, 4, 3, 305, 6.3e-5
- 15: 4, 10, 1289, 2, 15, 4, 3, 326, 6.3e-5
- 16: 6, 9, 1279, 4, 8, 4, 3, 382, 6.1e-5
- 17: 4, 10, 1246, 3, 12, 4, 3, 413, 5.7e-5
- 18: 4, 10, 1255, 3, 12, 4, 3, 416, 6.1e-5
- 19: 4, 10, 1334, 3, 12, 6, 2, 462, 6.3e-5
- 20: 4, 10, 1253, 4, 9, 4, 3, 514, 5.9e-5
- 21: 4, 10, 1265, 4, 9, 6, 2, 538, 6.3e-5
- 22: 4, 10, 1220, 5, 8, 6, 2, 615, 6.1e-5
- 23: 4, 10, 1225, 6, 7, 6, 2, 713, 6.2e-5
- 24: 4, 10, 1232, 7, 6, 6, 2, 813, 6.3e-5
- 25: 4, 10, 1248, 9, 5, 6, 2, 1019, 6.3e-5
- 26: 4, 10, 1279, 11, 4, 6, 2, 1243, 6.2e-5
- 27: 4, 10, 1225, 22, 2, 6, 2, 2244, 5.8e-5
- 28: 4, 10, 1288, 44, 1, 13, 1, 4643, 6.3e-5
# no solution starting from log norm2 = 29
- 3: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 3, 10, 1367, 1, 20, 3, 4, 174, 5.9e-5
- 1 : 3, 10, 1368, 1, 20, 3, 4, 175, 5.8e-5
- 2 : 3, 10, 1371, 1, 20, 3, 4, 175, 5.7e-5
- 3 : 3, 10, 1384, 1, 20, 3, 4, 176, 6.3e-5
- 4 : 4, 10, 1385, 1, 23, 3, 4, 231, 6.2e-5
- 5 : 4, 10, 1388, 1, 23, 3, 4, 231, 6.2e-5
- 6 : 4, 10, 1403, 1, 23, 3, 4, 233, 6.0e-5
- 7 : 3, 10, 1314, 2, 13, 4, 3, 253, 5.7e-5
- 8 : 3, 10, 1315, 2, 13, 4, 3, 253, 6.3e-5
- 9 : 3, 10, 1324, 2, 13, 4, 3, 255, 6.2e-5
- 10: 3, 10, 1378, 2, 13, 5, 3, 273, 6.3e-5
- 11: 3, 10, 1315, 3, 10, 4, 3, 330, 5.9e-5
- 12: 3, 10, 1321, 3, 10, 4, 3, 331, 6.0e-5
- 13: 4, 10, 1344, 2, 15, 4, 3, 340, 6.0e-5
- 14: 4, 10, 1406, 2, 15, 5, 3, 366, 6.3e-5
- 15: 3, 10, 1342, 4, 8, 6, 2, 431, 6.2e-5
- 16: 4, 10, 1335, 3, 12, 4, 3, 442, 6.1e-5
- 17: 4, 10, 1352, 3, 12, 4, 3, 447, 6.2e-5
- 18: 4, 10, 1334, 4, 9, 4, 3, 546, 6.2e-5
- 19: 4, 10, 1348, 4, 9, 4, 3, 551, 6.0e-5
- 20: 4, 10, 1293, 5, 8, 6, 2, 651, 6.1e-5
- 21: 4, 10, 1327, 5, 8, 6, 2, 667, 6.2e-5
- 22: 4, 10, 1319, 6, 7, 7, 2, 777, 6.3e-5
- 23: 4, 10, 1331, 7, 6, 7, 2, 888, 6.3e-5
- 24: 4, 10, 1368, 9, 5, 7, 2, 1126, 6.3e-5
- 25: 4, 10, 1311, 14, 3, 7, 2, 1592, 6.2e-5
- 26: 4, 10, 1318, 22, 2, 7, 2, 2424, 6.3e-5
# no solution starting from log norm2 = 27
- 4: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 2, 11, 1511, 1, 23, 3, 5, 290, 6.0e-5
- 1 : 2, 11, 1511, 1, 23, 3, 5, 290, 6.1e-5
- 2 : 2, 11, 1511, 1, 23, 3, 5, 290, 6.3e-5
- 3 : 2, 11, 1512, 1, 23, 3, 5, 290, 6.2e-5
- 4 : 2, 11, 1517, 1, 23, 3, 5, 291, 5.7e-5
- 5 : 2, 11, 1539, 1, 23, 3, 5, 295, 6.0e-5
- 6 : 2, 11, 1400, 2, 15, 5, 3, 415, 5.6e-5
- 7 : 2, 11, 1400, 2, 15, 5, 3, 415, 5.7e-5
- 8 : 2, 11, 1400, 2, 15, 5, 3, 415, 5.7e-5
- 9 : 2, 11, 1400, 2, 15, 5, 3, 415, 5.8e-5
- 10: 2, 11, 1400, 2, 15, 5, 3, 415, 6.3e-5
- 11: 2, 11, 1403, 2, 15, 5, 3, 416, 6.0e-5
- 12: 2, 11, 1415, 2, 15, 5, 3, 419, 6.1e-5
- 13: 2, 11, 1400, 3, 12, 5, 3, 538, 6.1e-5
- 14: 2, 11, 1402, 3, 12, 5, 3, 539, 5.8e-5
- 15: 2, 11, 1409, 3, 12, 5, 3, 541, 6.1e-5
- 16: 2, 11, 1465, 3, 12, 5, 3, 562, 6.2e-5
- 17: 2, 11, 1405, 4, 9, 5, 3, 663, 5.7e-5
- 18: 2, 11, 1424, 4, 9, 5, 3, 672, 6.0e-5
- 19: 2, 11, 1371, 5, 8, 7, 2, 789, 5.9e-5
- 20: 2, 11, 1375, 6, 7, 7, 2, 913, 6.0e-5
- 21: 2, 11, 1380, 7, 6, 7, 2, 1037, 6.0e-5
- 22: 2, 11, 1403, 8, 5, 7, 2, 1177, 6.2e-5
- 23: 2, 11, 1407, 11, 4, 7, 2, 1552, 6.1e-5
- 24: 2, 11, 1470, 15, 3, 8, 2, 2149, 6.3e-5
- 25: 2, 11, 1406, 43, 1, 15, 1, 5593, 6.3e-5
# no solution starting from log norm2 = 26
- 5: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 12, 1471, 1, 22, 5, 3, 395, 6.0e-5
- 1 : 1, 12, 1472, 1, 22, 5, 3, 395, 5.7e-5
- 2 : 1, 12, 1474, 1, 22, 5, 3, 396, 5.7e-5
- 3 : 1, 12, 1483, 1, 22, 5, 3, 398, 5.9e-5
- 4 : 1, 12, 1577, 1, 22, 6, 3, 434, 6.3e-5
- 5 : 1, 12, 1471, 2, 15, 5, 3, 567, 5.9e-5
- 6 : 1, 12, 1471, 2, 15, 5, 3, 567, 5.9e-5
- 7 : 1, 12, 1471, 2, 15, 5, 3, 567, 6.0e-5
- 8 : 1, 12, 1471, 2, 15, 5, 3, 567, 6.2e-5
- 9 : 1, 12, 1473, 2, 15, 5, 3, 568, 5.6e-5
- 10: 1, 12, 1478, 2, 15, 5, 3, 570, 5.8e-5
- 11: 1, 12, 1507, 2, 15, 5, 3, 581, 6.3e-5
- 12: 1, 12, 1472, 3, 11, 5, 3, 740, 5.9e-5
- 13: 1, 12, 1475, 3, 11, 5, 3, 742, 5.8e-5
- 14: 1, 12, 1489, 3, 11, 5, 3, 748, 5.8e-5
- 15: 1, 12, 1435, 4, 9, 7, 2, 912, 6.3e-5
- 16: 1, 12, 1483, 4, 9, 5, 3, 919, 5.9e-5
- 17: 1, 12, 1517, 4, 9, 8, 2, 976, 6.3e-5
- 18: 1, 12, 1519, 5, 8, 8, 2, 1155, 6.3e-5
- 19: 1, 12, 1454, 7, 6, 7, 2, 1436, 6.1e-5
- 20: 1, 12, 1449, 8, 5, 8, 2, 1612, 6.2e-5
- 21: 1, 12, 1468, 10, 4, 8, 2, 1977, 6.3e-5
- 22: 1, 12, 1474, 14, 3, 8, 2, 2676, 6.0e-5
- 23: 1, 12, 1451, 42, 1, 15, 1, 7475, 6.3e-5
# no solution starting from log norm2 = 24
- 6: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 13, 1637, 1, 22, 4, 4, 901, 5.9e-5
- 1 : 1, 13, 1643, 1, 22, 4, 4, 904, 6.2e-5
- 2 : 1, 13, 1686, 1, 22, 4, 4, 927, 6.3e-5
- 3 : 1, 13, 1602, 2, 15, 5, 3, 1308, 6.1e-5
- 4 : 1, 13, 1602, 2, 15, 5, 3, 1308, 6.1e-5
- 5 : 1, 13, 1602, 2, 15, 5, 3, 1308, 6.1e-5
- 6 : 1, 13, 1635, 2, 15, 4, 4, 1309, 6.2e-5
- 7 : 1, 13, 1636, 2, 15, 4, 4, 1310, 6.3e-5
- 8 : 1, 13, 1642, 2, 15, 4, 4, 1314, 5.9e-5
- 9 : 1, 13, 1673, 2, 15, 4, 4, 1339, 6.1e-5
- 10: 1, 13, 1603, 3, 11, 5, 3, 1710, 6.2e-5
- 11: 1, 13, 1607, 3, 11, 5, 3, 1714, 6.2e-5
- 12: 1, 13, 1594, 3, 11, 6, 3, 1725, 6.0e-5
- 13: 1, 13, 1645, 3, 11, 18, 1, 2088, 6.3e-5
- 14: 1, 13, 1548, 4, 9, 8, 2, 2112, 6.3e-5
- 15: 1, 13, 1678, 4, 9, 6, 3, 2234, 6.3e-5
- 16: 1, 13, 1553, 6, 7, 8, 2, 2895, 6.3e-5
- 17: 1, 13, 1557, 7, 6, 8, 2, 3292, 6.1e-5
- 18: 1, 13, 1563, 8, 5, 8, 2, 3695, 6.1e-5
- 19: 1, 13, 1581, 10, 4, 8, 2, 4528, 6.1e-5
- 20: 1, 13, 1588, 14, 3, 9, 2, 6160, 6.1e-5
- 21: 1, 13, 1554, 42, 1, 17, 1, 17102, 6.2e-5
# no solution starting from log norm2 = 22
- 7: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 14, 1714, 1, 22, 6, 3, 2099, 6.3e-5
- 1 : 1, 14, 1688, 2, 15, 6, 3, 2965, 5.8e-5
- 2 : 1, 14, 1688, 2, 15, 6, 3, 2965, 5.9e-5
- 3 : 1, 14, 1688, 2, 15, 6, 3, 2965, 5.9e-5
- 4 : 1, 14, 1688, 2, 15, 6, 3, 2965, 6.1e-5
- 5 : 1, 14, 1689, 2, 15, 6, 3, 2967, 6.2e-5
- 6 : 1, 14, 1694, 2, 15, 6, 3, 2975, 5.9e-5
- 7 : 1, 14, 1719, 2, 15, 6, 3, 3018, 6.2e-5
- 8 : 1, 14, 1688, 3, 11, 6, 3, 3862, 6.3e-5
- 9 : 1, 14, 1690, 3, 11, 6, 3, 3866, 6.3e-5
- 10: 1, 14, 1699, 3, 11, 6, 3, 3887, 6.2e-5
- 11: 1, 14, 1794, 3, 11, 6, 3, 4100, 6.3e-5
- 12: 1, 14, 1700, 4, 9, 6, 3, 4792, 6.1e-5
- 13: 1, 14, 1739, 4, 9, 10, 2, 5118, 6.3e-5
- 14: 1, 14, 1659, 6, 6, 9, 2, 6596, 6.0e-5
- 15: 1, 14, 1664, 7, 6, 9, 2, 7500, 6.3e-5
- 16: 1, 14, 1670, 8, 5, 9, 2, 8414, 5.9e-5
- 17: 1, 14, 1683, 10, 4, 9, 2, 10267, 6.3e-5
- 18: 1, 14, 1709, 14, 3, 9, 2, 14056, 6.3e-5
- 19: 1, 14, 1681, 41, 1, 19, 1, 38465, 6.2e-5
# no solution starting from log norm2 = 20
- 8: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 15, 1849, 2, 15, 5, 4, 6715, 6.1e-5
- 1 : 1, 15, 1849, 2, 15, 5, 4, 6715, 6.2e-5
- 2 : 1, 15, 1850, 2, 15, 5, 4, 6719, 5.7e-5
- 3 : 1, 15, 1851, 2, 15, 5, 4, 6722, 5.8e-5
- 4 : 1, 15, 1856, 2, 15, 5, 4, 6740, 5.8e-5
- 5 : 1, 15, 1883, 2, 15, 5, 4, 6836, 6.0e-5
- 6 : 1, 15, 1797, 3, 11, 7, 3, 8776, 6.2e-5
- 7 : 1, 15, 1799, 3, 11, 7, 3, 8786, 6.1e-5
- 8 : 1, 15, 1807, 3, 11, 7, 3, 8824, 6.0e-5
- 9 : 1, 15, 1872, 3, 11, 7, 3, 9137, 6.2e-5
- 10: 1, 15, 1809, 4, 9, 7, 3, 10869, 6.1e-5
- 11: 1, 15, 1876, 4, 9, 11, 2, 11736, 6.3e-5
- 12: 1, 15, 1859, 5, 7, 7, 3, 13257, 6.2e-5
- 13: 1, 15, 1823, 6, 6, 10, 2, 15396, 6.2e-5
- 14: 1, 15, 1779, 8, 5, 10, 2, 19030, 6.0e-5
- 15: 1, 15, 1792, 10, 4, 10, 2, 23200, 6.1e-5
- 16: 1, 15, 1825, 14, 3, 10, 2, 31838, 6.2e-5
- 17: 1, 15, 1805, 41, 1, 10, 2, 86317, 6.1e-5
# no solution starting from log norm2 = 18
- 9: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 16, 1966, 2, 14, 5, 4, 15001, 6.1e-5
- 1 : 1, 16, 1967, 2, 14, 5, 4, 15009, 6.2e-5
- 2 : 1, 16, 1908, 2, 14, 7, 3, 15044, 6.1e-5
- 3 : 1, 16, 1926, 2, 14, 7, 3, 15183, 6.2e-5
- 4 : 1, 16, 1904, 3, 11, 7, 3, 19535, 6.0e-5
- 5 : 1, 16, 1906, 3, 11, 7, 3, 19555, 6.0e-5
- 6 : 1, 16, 1914, 3, 11, 7, 3, 19636, 6.3e-5
- 7 : 1, 16, 1994, 3, 11, 7, 3, 20446, 6.3e-5
- 8 : 1, 16, 1918, 4, 9, 7, 3, 24232, 5.9e-5
- 9 : 1, 16, 1911, 5, 7, 7, 3, 28683, 5.9e-5
- 10: 1, 16, 1944, 5, 7, 7, 3, 29174, 6.2e-5
- 11: 1, 16, 1952, 6, 6, 7, 3, 33929, 6.2e-5
- 12: 1, 16, 1889, 8, 5, 11, 2, 42760, 6.2e-5
- 13: 1, 16, 1903, 10, 4, 11, 2, 52114, 6.2e-5
- 14: 1, 16, 1948, 14, 3, 11, 2, 71847, 6.3e-5
- 15: 1, 16, 1946, 40, 1, 11, 2, 191939, 6.3e-5
# no solution starting from log norm2 = 16
- 10: # bits
-ln2: k, N, n, br_l,br_b, ks_l,ks_b, cost, p_error
- 0 : 1, 17, 2014, 2, 14, 8, 3, 33745, 6.3e-5
- 1 : 1, 17, 2026, 2, 14, 8, 3, 33943, 5.9e-5
- 2 : 1, 17, 2012, 3, 11, 8, 3, 43772, 5.9e-5
- 3 : 1, 17, 2014, 3, 11, 8, 3, 43815, 5.8e-5
- 4 : 1, 17, 2022, 3, 11, 8, 3, 43987, 6.1e-5
- 5 : 1, 17, 2044, 3, 11, 12, 2, 46506, 6.3e-5
- 6 : 1, 17, 2026, 4, 9, 8, 3, 54203, 5.9e-5
- 7 : 1, 17, 2017, 5, 7, 8, 3, 64050, 6.0e-5
- 8 : 1, 17, 2040, 5, 7, 8, 3, 64774, 6.2e-5
- 9 : 1, 17, 2046, 6, 6, 8, 3, 75193, 6.3e-5
- 10: 1, 17, 2010, 8, 5, 11, 2, 95488, 6.1e-5
- 11: 1, 17, 2016, 10, 4, 12, 2, 116436, 6.2e-5
- 12: 1, 17, 2029, 19, 2, 23, 1, 214072, 6.3e-5
- 13: 1, 17, 2036, 40, 1, 12, 2, 422986, 6.3e-5
# no solution starting from log norm2 = 14