/* Copyright (c) 2026 Nenad Mićić * SPDX-License-Identifier: Apache-2.0 */ /* * ktuplet_pattern.c — pattern table and helper implementations. * Generated: 2026-05-10 * * Catalog source of truth: tools/patterns/catalog/k{NN}_d{DDD}.json * Catalog generator: tools/patterns/pattern_enum (C/OpenMP) * Header generator: tools/gen_pattern_header.py * * Authoritative reference for prime k-tuplet patterns and Hardy-Littlewood * constants: https://pzktupel.de/ktpatt_hl.php (Norman Luhn) * * The tools in this repo (pattern_enum, gen_pattern_header.py) are a * convenience: they emit the same admissible patterns in machine-readable * JSON for engine consumption. They are NOT peer-reviewed; if there is any * discrepancy between this generated catalog and pzktupel.de, the canonical * pzktupel.de listing is correct and our tools have a bug. Cross-check * before publishing or relying on any pattern. * * Do not edit by hand. Run: python3 tools/gen_pattern_header.py */ #include "ktuplet_pattern.h" #include const KTupletPattern KT_PATTERNS[] = { /* KT3_P0 from k03_d006.json */ { 3, 6, {0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT3_P0" }, /* KT3_P1 from k03_d006.json */ { 3, 6, {0, 4, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT3_P1" }, /* KT4_P0 from k04_d008.json */ { 4, 8, {0, 2, 6, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT4_P0" }, /* KT5_P0 from k05_d012.json */ { 5, 12, {0, 2, 6, 8, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT5_P0" }, /* KT5_P1 from k05_d012.json */ { 5, 12, {0, 4, 6, 10, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT5_P1" }, /* KT6_P0 from k06_d016.json */ { 6, 16, {0, 4, 6, 10, 12, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT6_P0" }, /* KT7_P0 from k07_d020.json */ { 7, 20, {0, 2, 6, 8, 12, 18, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT7_P0" }, /* KT7_P1 from k07_d020.json */ { 7, 20, {0, 2, 8, 12, 14, 18, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT7_P1" }, /* KT8_P0 from k08_d026.json */ { 8, 26, {0, 2, 6, 8, 12, 18, 20, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT8_P0" }, /* KT8_P1 from k08_d026.json */ { 8, 26, {0, 2, 6, 12, 14, 20, 24, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT8_P1" }, /* KT8_P2 from k08_d026.json */ { 8, 26, {0, 6, 8, 14, 18, 20, 24, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT8_P2" }, /* KT9_P0 from k09_d030.json */ { 9, 30, {0, 2, 6, 8, 12, 18, 20, 26, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT9_P0" }, /* KT9_P1 from k09_d030.json */ { 9, 30, {0, 2, 6, 12, 14, 20, 24, 26, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT9_P1" }, /* KT9_P2 from k09_d030.json */ { 9, 30, {0, 4, 6, 10, 16, 18, 24, 28, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT9_P2" }, /* KT9_P3 from k09_d030.json */ { 9, 30, {0, 4, 10, 12, 18, 22, 24, 28, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT9_P3" }, /* KT10_P0 from k10_d032.json */ { 10, 32, {0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT10_P0" }, /* KT10_P1 from k10_d032.json */ { 10, 32, {0, 2, 6, 12, 14, 20, 24, 26, 30, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT10_P1" }, /* KT11_P0 from k11_d036.json */ { 11, 36, {0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT11_P0" }, /* KT11_P1 from k11_d036.json */ { 11, 36, {0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT11_P1" }, /* KT12_P0 from k12_d042.json */ { 12, 42, {0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT12_P0" }, /* KT12_P1 from k12_d042.json */ { 12, 42, {0, 6, 10, 12, 16, 22, 24, 30, 34, 36, 40, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT12_P1" }, /* KT13_P0 from k13_d048.json */ { 13, 48, {0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT13_P0" }, /* KT13_P1 from k13_d048.json */ { 13, 48, {0, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT13_P1" }, /* KT13_P2 from k13_d048.json */ { 13, 48, {0, 2, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT13_P2" }, /* KT13_P3 from k13_d048.json */ { 13, 48, {0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36, 46, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT13_P3" }, /* KT13_P4 from k13_d048.json */ { 13, 48, {0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT13_P4" }, /* KT13_P5 from k13_d048.json */ { 13, 48, {0, 6, 12, 16, 18, 22, 28, 30, 36, 40, 42, 46, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT13_P5" }, /* KT14_P0 from k14_d050.json */ { 14, 50, {0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT14_P0" }, /* KT14_P1 from k14_d050.json */ { 14, 50, {0, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT14_P1" }, /* KT15_P0 from k15_d056.json */ { 15, 56, {0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT15_P0" }, /* KT15_P1 from k15_d056.json */ { 15, 56, {0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 50, 54, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT15_P1" }, /* KT15_P2 from k15_d056.json */ { 15, 56, {0, 2, 6, 12, 14, 20, 26, 30, 32, 36, 42, 44, 50, 54, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT15_P2" }, /* KT15_P3 from k15_d056.json */ { 15, 56, {0, 6, 8, 14, 20, 24, 26, 30, 36, 38, 44, 48, 50, 54, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT15_P3" }, /* KT16_P0 from k16_d060.json */ { 16, 60, {0, 2, 6, 12, 14, 20, 26, 30, 32, 36, 42, 44, 50, 54, 56, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT16_P0" }, /* KT16_P1 from k16_d060.json */ { 16, 60, {0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT16_P1" }, /* KT17_P0 from k17_d066.json */ { 17, 66, {0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 50, 54, 56, 62, 66, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT17_P0" }, /* KT17_P1 from k17_d066.json */ { 17, 66, {0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT17_P1" }, /* KT17_P2 from k17_d066.json */ { 17, 66, {0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT17_P2" }, /* KT17_P3 from k17_d066.json */ { 17, 66, {0, 6, 8, 12, 18, 20, 26, 32, 36, 38, 42, 48, 50, 56, 60, 62, 66, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT17_P3" }, /* KT18_P0 from k18_d070.json */ { 18, 70, {0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT18_P0" }, /* KT18_P1 from k18_d070.json */ { 18, 70, {0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT18_P1" }, /* KT19_P0 from k19_d076.json */ { 19, 76, {0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 54, 60, 66, 70, 72, 76, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT19_P0" }, /* KT19_P1 from k19_d076.json */ { 19, 76, {0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70, 76, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT19_P1" }, /* KT19_P2 from k19_d076.json */ { 19, 76, {0, 4, 6, 10, 16, 22, 24, 30, 34, 36, 42, 46, 52, 60, 64, 66, 70, 72, 76, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT19_P2" }, /* KT19_P3 from k19_d076.json */ { 19, 76, {0, 6, 10, 16, 18, 22, 28, 30, 36, 42, 46, 48, 52, 58, 60, 66, 70, 72, 76, 0, 0, 0, 0, 0, 0, 0, 0, 0}, "KT19_P3" }, /* KT20_P0 from k20_d080.json */ { 20, 80, {0, 2, 6, 8, 12, 20, 26, 30, 36, 38, 42, 48, 50, 56, 62, 66, 68, 72, 78, 80, 0, 0, 0, 0, 0, 0, 0, 0}, "KT20_P0" }, /* KT20_P1 from k20_d080.json */ { 20, 80, {0, 2, 8, 12, 14, 18, 24, 30, 32, 38, 42, 44, 50, 54, 60, 68, 72, 74, 78, 80, 0, 0, 0, 0, 0, 0, 0, 0}, "KT20_P1" }, /* KT21_P0 from k21_d084.json */ { 21, 84, {0, 2, 8, 12, 14, 18, 24, 30, 32, 38, 42, 44, 50, 54, 60, 68, 72, 74, 78, 80, 84, 0, 0, 0, 0, 0, 0, 0}, "KT21_P0" }, /* KT21_P1 from k21_d084.json */ { 21, 84, {0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 54, 60, 66, 70, 72, 76, 82, 84, 0, 0, 0, 0, 0, 0, 0}, "KT21_P1" }, /* KT22_P0 from k22_d090.json */ { 22, 90, {0, 2, 6, 8, 12, 20, 26, 30, 36, 38, 42, 48, 50, 56, 62, 66, 68, 72, 78, 80, 86, 90, 0, 0, 0, 0, 0, 0}, "KT22_P0" }, /* KT22_P1 from k22_d090.json */ { 22, 90, {0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 54, 60, 66, 70, 72, 76, 82, 84, 90, 0, 0, 0, 0, 0, 0}, "KT22_P1" }, /* KT22_P2 from k22_d090.json */ { 22, 90, {0, 4, 10, 12, 18, 22, 24, 28, 34, 40, 42, 48, 52, 54, 60, 64, 70, 78, 82, 84, 88, 90, 0, 0, 0, 0, 0, 0}, "KT22_P2" }, /* KT22_P3 from k22_d090.json */ { 22, 90, {0, 6, 8, 14, 18, 20, 24, 30, 36, 38, 44, 48, 50, 56, 60, 66, 74, 78, 80, 84, 86, 90, 0, 0, 0, 0, 0, 0}, "KT22_P3" }, /* KT23_P0 from k23_d094.json */ { 23, 94, {0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 54, 60, 66, 70, 72, 76, 82, 84, 90, 94, 0, 0, 0, 0, 0}, "KT23_P0" }, /* KT23_P1 from k23_d094.json */ { 23, 94, {0, 4, 10, 12, 18, 22, 24, 28, 34, 40, 42, 48, 52, 54, 60, 64, 70, 78, 82, 84, 88, 90, 94, 0, 0, 0, 0, 0}, "KT23_P1" }, /* KT24_P0 from k24_d100.json */ { 24, 100, {0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 60, 66, 70, 72, 76, 82, 84, 90, 94, 96, 100, 0, 0, 0, 0}, "KT24_P0" }, /* KT24_P1 from k24_d100.json */ { 24, 100, {0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 48, 54, 58, 60, 66, 70, 76, 84, 88, 90, 94, 96, 100, 0, 0, 0, 0}, "KT24_P1" }, /* KT24_P2 from k24_d100.json */ { 24, 100, {0, 4, 6, 12, 16, 24, 30, 34, 40, 42, 46, 52, 54, 60, 66, 70, 72, 76, 82, 84, 90, 94, 96, 100, 0, 0, 0, 0}, "KT24_P2" }, /* KT24_P3 from k24_d100.json */ { 24, 100, {0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70, 76, 84, 88, 94, 96, 100, 0, 0, 0, 0}, "KT24_P3" }, /* KT25_P0 from k25_d110.json */ { 25, 110, {0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50, 56, 62, 68, 72, 78, 86, 90, 96, 98, 102, 110, 0, 0, 0}, "KT25_P0" }, /* KT25_P1 from k25_d110.json */ { 25, 110, {0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 50, 56, 62, 68, 72, 78, 86, 90, 92, 96, 98, 102, 110, 0, 0, 0}, "KT25_P1" }, /* KT25_P2 from k25_d110.json */ { 25, 110, {0, 2, 6, 8, 12, 20, 26, 30, 36, 38, 42, 48, 50, 56, 66, 68, 72, 78, 80, 86, 90, 92, 98, 108, 110, 0, 0, 0}, "KT25_P2" }, /* KT25_P3 from k25_d110.json */ { 25, 110, {0, 2, 6, 8, 12, 20, 26, 30, 36, 38, 42, 48, 56, 62, 66, 68, 72, 78, 80, 86, 90, 92, 96, 108, 110, 0, 0, 0}, "KT25_P3" }, /* KT25_P4 from k25_d110.json */ { 25, 110, {0, 2, 6, 8, 12, 20, 26, 30, 36, 38, 42, 48, 56, 66, 68, 72, 78, 80, 86, 90, 92, 96, 98, 108, 110, 0, 0, 0}, "KT25_P4" }, /* KT25_P5 from k25_d110.json */ { 25, 110, {0, 2, 6, 8, 12, 20, 26, 30, 36, 38, 42, 50, 56, 62, 66, 68, 72, 78, 80, 86, 90, 92, 96, 108, 110, 0, 0, 0}, "KT25_P5" }, /* KT25_P6 from k25_d110.json */ { 25, 110, {0, 2, 6, 8, 12, 20, 26, 30, 36, 38, 42, 50, 56, 66, 68, 72, 78, 80, 86, 90, 92, 96, 98, 108, 110, 0, 0, 0}, "KT25_P6" }, /* KT25_P7 from k25_d110.json */ { 25, 110, {0, 2, 6, 12, 14, 20, 24, 26, 30, 32, 42, 44, 54, 56, 60, 66, 72, 74, 80, 86, 90, 96, 102, 104, 110, 0, 0, 0}, "KT25_P7" }, /* KT25_P8 from k25_d110.json */ { 25, 110, {0, 2, 8, 12, 14, 18, 24, 30, 32, 38, 42, 44, 50, 54, 60, 68, 72, 74, 78, 80, 84, 98, 102, 108, 110, 0, 0, 0}, "KT25_P8" }, /* KT25_P9 from k25_d110.json */ { 25, 110, {0, 2, 8, 12, 26, 30, 32, 36, 38, 42, 50, 56, 60, 66, 68, 72, 78, 80, 86, 92, 96, 98, 102, 108, 110, 0, 0, 0}, "KT25_P9" }, /* KT25_P10 from k25_d110.json */ { 25, 110, {0, 2, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 54, 60, 68, 72, 74, 80, 84, 90, 98, 102, 104, 108, 110, 0, 0, 0}, "KT25_P10" }, /* KT25_P11 from k25_d110.json */ { 25, 110, {0, 2, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 54, 62, 68, 72, 74, 80, 84, 90, 98, 102, 104, 108, 110, 0, 0, 0}, "KT25_P11" }, /* KT25_P12 from k25_d110.json */ { 25, 110, {0, 2, 12, 18, 20, 24, 30, 32, 38, 42, 44, 54, 60, 62, 68, 72, 74, 80, 84, 90, 98, 102, 104, 108, 110, 0, 0, 0}, "KT25_P12" }, /* KT25_P13 from k25_d110.json */ { 25, 110, {0, 2, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 54, 60, 68, 72, 74, 80, 84, 90, 98, 102, 104, 108, 110, 0, 0, 0}, "KT25_P13" }, /* KT25_P14 from k25_d110.json */ { 25, 110, {0, 2, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 54, 62, 68, 72, 74, 80, 84, 90, 98, 102, 104, 108, 110, 0, 0, 0}, "KT25_P14" }, /* KT25_P15 from k25_d110.json */ { 25, 110, {0, 6, 8, 14, 20, 24, 30, 36, 38, 44, 50, 54, 56, 66, 68, 78, 80, 84, 86, 90, 96, 98, 104, 108, 110, 0, 0, 0}, "KT25_P15" }, /* KT25_P16 from k25_d110.json */ { 25, 110, {0, 8, 12, 14, 18, 20, 24, 32, 38, 42, 48, 54, 60, 68, 74, 78, 80, 84, 90, 92, 98, 102, 104, 108, 110, 0, 0, 0}, "KT25_P16" }, /* KT25_P17 from k25_d110.json */ { 25, 110, {0, 8, 12, 14, 20, 24, 32, 38, 42, 48, 54, 60, 62, 68, 74, 78, 80, 84, 90, 92, 98, 102, 104, 108, 110, 0, 0, 0}, "KT25_P17" }, /* KT26_P0 from k26_d114.json */ { 26, 114, {0, 2, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 54, 62, 68, 72, 74, 80, 84, 90, 98, 102, 104, 108, 110, 114, 0, 0}, "KT26_P0" }, /* KT26_P1 from k26_d114.json */ { 26, 114, {0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 60, 66, 70, 72, 76, 82, 84, 90, 94, 96, 100, 112, 114, 0, 0}, "KT26_P1" }, /* KT27_P0 from k27_d120.json */ { 27, 120, {0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50, 56, 62, 68, 72, 78, 86, 90, 96, 98, 102, 110, 116, 120, 0}, "KT27_P0" }, /* KT27_P1 from k27_d120.json */ { 27, 120, {0, 2, 6, 12, 14, 20, 26, 32, 36, 42, 44, 50, 54, 56, 60, 62, 72, 84, 86, 90, 92, 102, 104, 110, 114, 116, 120, 0}, "KT27_P1" }, /* KT27_P2 from k27_d120.json */ { 27, 120, {0, 2, 6, 14, 20, 26, 32, 36, 42, 44, 50, 54, 60, 62, 72, 74, 84, 86, 90, 92, 96, 102, 104, 110, 114, 116, 120, 0}, "KT27_P2" }, /* KT27_P3 from k27_d120.json */ { 27, 120, {0, 2, 8, 12, 26, 30, 32, 36, 38, 42, 50, 56, 60, 66, 68, 72, 78, 80, 86, 92, 96, 98, 102, 108, 110, 116, 120, 0}, "KT27_P3" }, /* KT27_P4 from k27_d120.json */ { 27, 120, {0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36, 46, 48, 58, 60, 66, 70, 76, 78, 84, 88, 94, 100, 106, 114, 118, 120, 0}, "KT27_P4" }, /* KT27_P5 from k27_d120.json */ { 27, 120, {0, 4, 6, 10, 16, 18, 28, 30, 34, 36, 48, 58, 60, 64, 66, 70, 76, 78, 84, 88, 94, 100, 106, 108, 114, 118, 120, 0}, "KT27_P5" }, /* KT27_P6 from k27_d120.json */ { 27, 120, {0, 4, 10, 12, 18, 22, 24, 28, 34, 40, 42, 48, 52, 54, 60, 64, 70, 78, 82, 84, 88, 90, 94, 108, 112, 118, 120, 0}, "KT27_P6" }, /* KT27_P7 from k27_d120.json */ { 27, 120, {0, 4, 10, 18, 22, 24, 30, 34, 42, 48, 52, 58, 64, 70, 72, 78, 84, 88, 90, 94, 100, 102, 108, 112, 114, 118, 120, 0}, "KT27_P7" }, /* KT28_P0 from k28_d126.json */ { 28, 126, {0, 2, 6, 8, 12, 20, 26, 30, 36, 38, 42, 48, 56, 66, 68, 72, 78, 80, 86, 90, 92, 96, 98, 108, 110, 120, 122, 126}, "KT28_P0" }, /* KT28_P1 from k28_d126.json */ { 28, 126, {0, 2, 6, 12, 14, 24, 26, 30, 32, 44, 54, 56, 60, 62, 66, 72, 74, 80, 84, 90, 96, 102, 104, 110, 114, 116, 122, 126}, "KT28_P1" }, /* KT28_P2 from k28_d126.json */ { 28, 126, {0, 2, 6, 14, 20, 26, 32, 36, 42, 44, 50, 54, 60, 62, 72, 74, 84, 86, 90, 92, 96, 102, 104, 110, 114, 116, 120, 126}, "KT28_P2" }, /* KT28_P3 from k28_d126.json */ { 28, 126, {0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36, 46, 48, 58, 60, 66, 70, 76, 78, 84, 88, 94, 100, 106, 114, 118, 120, 126}, "KT28_P3" }, /* KT28_P4 from k28_d126.json */ { 28, 126, {0, 4, 6, 10, 16, 18, 28, 30, 34, 36, 48, 58, 60, 64, 66, 70, 76, 78, 84, 88, 94, 100, 106, 108, 114, 118, 120, 126}, "KT28_P4" }, /* KT28_P5 from k28_d126.json */ { 28, 126, {0, 4, 6, 16, 18, 28, 30, 34, 36, 40, 46, 48, 54, 58, 60, 70, 78, 84, 88, 90, 96, 100, 106, 114, 118, 120, 124, 126}, "KT28_P5" }, /* KT28_P6 from k28_d126.json */ { 28, 126, {0, 4, 10, 12, 16, 22, 24, 30, 36, 42, 46, 52, 54, 60, 64, 66, 70, 72, 82, 94, 96, 100, 102, 112, 114, 120, 124, 126}, "KT28_P6" }, /* KT28_P7 from k28_d126.json */ { 28, 126, {0, 6, 8, 12, 18, 20, 26, 32, 38, 42, 48, 50, 56, 60, 62, 66, 68, 78, 90, 92, 96, 98, 108, 110, 116, 120, 122, 126}, "KT28_P7" }, /* KT28_P8 from k28_d126.json */ { 28, 126, {0, 6, 8, 12, 20, 26, 32, 38, 42, 48, 50, 56, 60, 66, 68, 78, 80, 90, 92, 96, 98, 102, 108, 110, 116, 120, 122, 126}, "KT28_P8" }, /* KT28_P9 from k28_d126.json */ { 28, 126, {0, 6, 10, 12, 16, 22, 24, 30, 34, 36, 40, 42, 52, 54, 64, 66, 72, 76, 82, 84, 90, 94, 100, 106, 112, 120, 124, 126}, "KT28_P9" }, }; const int KT_PATTERNS_COUNT = 97; /* Forbidden residues for pattern pat at prime q. * Formula: ((q - (b_i % q)) % q) for each offset b_i, deduplicated. */ int kt_pattern_forbidden_residues(const KTupletPattern* pat, uint32_t q, uint32_t* out) { int count = 0; for (int i = 0; i < pat->k; i++) { uint32_t r = (q - ((uint32_t)pat->offsets[i] % q)) % q; int dup = 0; for (int j = 0; j < count; j++) { if (out[j] == r) { dup = 1; break; } } if (!dup) out[count++] = r; } return count; } int kt_pattern_is_admissible(const KTupletPattern* pat, int q_max, int* bad_q) { uint32_t buf[KT_MAX_K]; for (int q = 2; q <= q_max; q++) { int is_prime = 1; for (int d = 2; d * d <= q; d++) { if (q % d == 0) { is_prime = 0; break; } } if (!is_prime) continue; int cnt = kt_pattern_forbidden_residues(pat, (uint32_t)q, buf); if (cnt >= q) { if (bad_q) *bad_q = q; return 0; } } return 1; } const KTupletPattern* kt_pattern_by_name(const char* name) { for (int i = 0; i < KT_PATTERNS_COUNT; i++) if (strcmp(KT_PATTERNS[i].name, name) == 0) return &KT_PATTERNS[i]; return NULL; } const KTupletPattern* kt_pattern_match(int k, const int* offsets) { for (int i = 0; i < KT_PATTERNS_COUNT; i++) { if (KT_PATTERNS[i].k != k) continue; int match = 1; for (int j = 0; j < k; j++) if (KT_PATTERNS[i].offsets[j] != offsets[j]) { match = 0; break; } if (match) return &KT_PATTERNS[i]; } return NULL; }