Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 | /** * Precomputed table of "landmark" primes — notable primes that should remain * visible even when zoomed far out (beyond the range where live sieve scanning * is practical). * * Sources: OEIS A002386 (maximal prime gaps), A000668 (Mersenne primes), * notable palindromic primes. */ export type PrimeInterestTag = | 'twin' | 'cousin' | 'sexy' | 'triplet' | 'quadruplet' | 'palindrome' | 'gap-record' | 'high-merit' | 'mersenne' | 'sophie-germain' export interface LandmarkPrime { value: number score: number tags: PrimeInterestTag[] note?: string } /** * Sorted by value for binary search. * * Includes: * - Mersenne primes up to 2^31-1 * - Maximal prime gap endpoints (from OEIS A002386 / A005250) * - Notable palindromic primes * - First-occurrence gap milestones */ /** Helper to ensure tag arrays are properly typed */ function lp(value: number, score: number, tags: PrimeInterestTag[], note?: string): LandmarkPrime { return note ? { value, score, tags, note } : { value, score, tags } } export const LANDMARK_PRIMES: LandmarkPrime[] = [ // Mersenne primes (score 100+) lp(3, 110, ['mersenne', 'twin'], 'Mersenne prime 2²−1'), lp(7, 105, ['mersenne', 'twin'], 'Mersenne prime 2³−1'), lp(31, 105, ['mersenne', 'twin'], 'Mersenne prime 2⁵−1'), lp(127, 100, ['mersenne'], 'Mersenne prime 2⁷−1'), lp(8191, 100, ['mersenne'], 'Mersenne prime 2¹³−1'), lp(131071, 100, ['mersenne'], 'Mersenne prime 2¹⁷−1'), lp(524287, 100, ['mersenne'], 'Mersenne prime 2¹⁹−1'), lp(2147483647, 100, ['mersenne'], 'Mersenne prime 2³¹−1'), // Maximal prime gap records (OEIS A002386: primes starting record gaps) // Format: prime before gap, prime after gap, gap size lp(2, 40, ['gap-record'], 'Record gap of 1 (to 3)'), lp(7, 40, ['gap-record', 'mersenne'], 'Record gap of 4 (to 11)'), lp(11, 30, ['gap-record'], 'End of record gap of 4'), lp(23, 35, ['gap-record'], 'Record gap of 6 (to 29)'), lp(29, 30, ['gap-record', 'twin'], 'End of record gap of 6'), lp(89, 35, ['gap-record'], 'Record gap of 8 (to 97)'), lp(97, 30, ['gap-record'], 'End of record gap of 8'), lp(113, 38, ['gap-record'], 'Record gap of 14 (to 127)'), lp(523, 38, ['gap-record'], 'Record gap of 18 (to 541)'), lp(541, 30, ['gap-record'], 'End of record gap of 18'), lp(887, 38, ['gap-record'], 'Record gap of 20 (to 907)'), lp(907, 30, ['gap-record'], 'End of record gap of 20'), lp(1129, 38, ['gap-record'], 'Record gap of 22 (to 1151)'), lp(1151, 30, ['gap-record'], 'End of record gap of 22'), lp(1327, 42, ['gap-record'], 'Record gap of 34 (to 1361)'), lp(1361, 32, ['gap-record'], 'End of record gap of 34'), lp(9551, 42, ['gap-record'], 'Record gap of 36 (to 9587)'), lp(9587, 32, ['gap-record'], 'End of record gap of 36'), lp(15683, 44, ['gap-record'], 'Record gap of 44 (to 15727)'), lp(15727, 34, ['gap-record'], 'End of record gap of 44'), lp(19609, 46, ['gap-record'], 'Record gap of 52 (to 19661)'), lp(19661, 36, ['gap-record'], 'End of record gap of 52'), lp(31397, 50, ['gap-record'], 'Record gap of 72 (to 31469)'), lp(31469, 40, ['gap-record'], 'End of record gap of 72'), lp(155921, 52, ['gap-record'], 'Record gap of 86 (to 156007)'), lp(156007, 42, ['gap-record'], 'End of record gap of 86'), lp(360653, 54, ['gap-record'], 'Record gap of 96 (to 360749)'), lp(360749, 44, ['gap-record'], 'End of record gap of 96'), lp(370261, 56, ['gap-record'], 'Record gap of 112 (to 370373)'), lp(370373, 46, ['gap-record'], 'End of record gap of 112'), lp(492113, 56, ['gap-record'], 'Record gap of 114 (to 492227)'), lp(492227, 46, ['gap-record'], 'End of record gap of 114'), lp(1349533, 58, ['gap-record'], 'Record gap of 118 (to 1349651)'), lp(1349651, 48, ['gap-record'], 'End of record gap of 118'), lp(1357201, 60, ['gap-record'], 'Record gap of 132 (to 1357333)'), lp(1357333, 50, ['gap-record'], 'End of record gap of 132'), lp(2010733, 62, ['gap-record'], 'Record gap of 148 (to 2010881)'), lp(2010881, 52, ['gap-record'], 'End of record gap of 148'), lp(4652353, 62, ['gap-record'], 'Record gap of 154 (to 4652507)'), lp(4652507, 52, ['gap-record'], 'End of record gap of 154'), lp(17051707, 65, ['gap-record'], 'Record gap of 180 (to 17051887)'), lp(17051887, 55, ['gap-record'], 'End of record gap of 180'), lp(20831323, 68, ['gap-record'], 'Record gap of 210 (to 20831533)'), lp(20831533, 58, ['gap-record'], 'End of record gap of 210'), lp(47326693, 68, ['gap-record'], 'Record gap of 220 (to 47326913)'), lp(47326913, 58, ['gap-record'], 'End of record gap of 220'), lp(122164747, 68, ['gap-record'], 'Record gap of 222 (to 122164969)'), lp(122164969, 58, ['gap-record'], 'End of record gap of 222'), lp(189695659, 70, ['gap-record'], 'Record gap of 234 (to 189695893)'), lp(189695893, 60, ['gap-record'], 'End of record gap of 234'), lp(191912783, 72, ['gap-record'], 'Record gap of 248 (to 191913031)'), lp(191913031, 62, ['gap-record'], 'End of record gap of 248'), lp(387096133, 72, ['gap-record'], 'Record gap of 250 (to 387096383)'), lp(387096383, 62, ['gap-record'], 'End of record gap of 250'), lp(436273009, 75, ['gap-record'], 'Record gap of 282 (to 436273291)'), lp(436273291, 65, ['gap-record'], 'End of record gap of 282'), lp(2300942549, 75, ['gap-record'], 'Record gap of 288 (to 2300942837)'), lp(2300942837, 65, ['gap-record'], 'End of record gap of 288'), lp(3842610773, 75, ['gap-record'], 'Record gap of 292 (to 3842611065)'), lp(3842611063, 65, ['gap-record'], 'End of record gap of 292'), lp(4302407359, 78, ['gap-record'], 'Record gap of 320 (to 4302407679)'), lp(4302407677, 68, ['gap-record'], 'End of record gap of 320'), // Notable palindromic primes (various digit counts) lp(11, 25, ['palindrome'], 'Smallest 2-digit palindrome prime'), lp(101, 25, ['palindrome'], 'Smallest 3-digit palindrome prime'), lp(131, 22, ['palindrome'], 'Palindrome prime'), lp(151, 22, ['palindrome'], 'Palindrome prime'), lp(181, 22, ['palindrome'], 'Palindrome prime'), lp(191, 22, ['palindrome'], 'Palindrome prime'), lp(313, 22, ['palindrome'], 'Palindrome prime'), lp(353, 22, ['palindrome'], 'Palindrome prime'), lp(373, 22, ['palindrome'], 'Palindrome prime'), lp(383, 22, ['palindrome'], 'Palindrome prime'), lp(727, 22, ['palindrome'], 'Palindrome prime'), lp(757, 22, ['palindrome'], 'Palindrome prime'), lp(787, 22, ['palindrome'], 'Palindrome prime'), lp(797, 22, ['palindrome'], 'Palindrome prime'), lp(919, 22, ['palindrome'], 'Palindrome prime'), lp(929, 22, ['palindrome'], 'Palindrome prime'), lp(10301, 28, ['palindrome'], 'Smallest 5-digit palindrome prime'), lp(1003001, 30, ['palindrome'], '7-digit palindrome prime'), lp(100030001, 32, ['palindrome'], '9-digit palindrome prime'), // First occurrence of gap ≥ N milestones lp(396733, 45, ['gap-record'], 'First prime gap ≥ 100 (gap 100)'), lp(396833, 35, ['gap-record'], 'End of first gap ≥ 100'), lp(2010733, 50, ['gap-record'], 'First prime gap ≥ 148'), lp(20831323, 55, ['gap-record'], 'First prime gap ≥ 200 (gap 210)'), ].sort((a, b) => a.value - b.value) // Deduplicate: if same value appears multiple times, merge tags and keep highest score const deduped = new Map<number, LandmarkPrime>() for (const entry of LANDMARK_PRIMES) { const existing = deduped.get(entry.value) if (existing) { existing.score = Math.max(existing.score, entry.score) for (const tag of entry.tags) { if (!existing.tags.includes(tag)) existing.tags.push(tag) } // Prefer the note from the higher-scored entry if (entry.score >= existing.score && entry.note) existing.note = entry.note } else { deduped.set(entry.value, { ...entry, tags: [...entry.tags] }) } } const DEDUPLICATED_LANDMARKS: LandmarkPrime[] = [...deduped.values()].sort( (a, b) => a.value - b.value ) /** * Binary search for landmark primes in [left, right]. */ export function getLandmarksInRange(left: number, right: number): LandmarkPrime[] { const landmarks = DEDUPLICATED_LANDMARKS if (landmarks.length === 0) return [] // Binary search for first landmark >= left let lo = 0 let hi = landmarks.length while (lo < hi) { const mid = (lo + hi) >>> 1 if (landmarks[mid].value < left) lo = mid + 1 else hi = mid } const result: LandmarkPrime[] = [] for (let i = lo; i < landmarks.length && landmarks[i].value <= right; i++) { result.push(landmarks[i]) } return result } |