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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 | /** * Prime interestingness scoring system. * * Each visible prime gets a score based on its mathematical properties. * At high zoom all primes are shown; at low zoom only primes above a * density-adaptive threshold appear. */ import { computeVisiblePrimes, smallestPrimeFactor } from './sieve' import { MERSENNE_PRIMES } from './specialPrimes' import type { PrimeInterestTag, LandmarkPrime } from './landmarkPrimes' import { getLandmarksInRange } from './landmarkPrimes' export type { PrimeInterestTag } export interface InterestingPrime { value: number score: number tags: PrimeInterestTag[] note?: string } // --- Helpers --- function isPrime(n: number): boolean { return n >= 2 && smallestPrimeFactor(n) === n } function isPalindrome(n: number): boolean { const s = String(n) const len = s.length for (let i = 0; i < len >>> 1; i++) { if (s[i] !== s[len - 1 - i]) return false } return true } // --- Gap record computation (cached) --- let gapRecordPrimes: Set<number> | null = null let gapRecordSizes: Map<number, number> | null = null /** * Lazily compute gap record primes from the sieve range (primes up to ~100K). * A gap-record prime is one that starts a gap larger than all previous gaps. */ function ensureGapRecords(): { primes: Set<number>; sizes: Map<number, number> } { if (gapRecordPrimes && gapRecordSizes) { return { primes: gapRecordPrimes, sizes: gapRecordSizes } } gapRecordPrimes = new Set<number>() gapRecordSizes = new Map<number, number>() let maxGap = 0 let prevPrime = 2 // Scan sieve range for (let n = 3; n < 100_001; n++) { if (!isPrime(n)) continue const gap = n - prevPrime if (gap > maxGap) { maxGap = gap gapRecordPrimes.add(prevPrime) gapRecordPrimes.add(n) gapRecordSizes.set(prevPrime, gap) } prevPrime = n } return { primes: gapRecordPrimes, sizes: gapRecordSizes } } // --- Scoring --- /** * Score a single prime based on its mathematical properties. * * | Tag | Score | * |------------------|--------| * | Base (every) | 1 | * | Twin | +10 | * | Cousin | +5 | * | Sexy | +3 | * | Triplet member | +30 | * | Quadruplet member| +50 | * | Palindrome | +20 | * | Gap record | +30 | * | High merit (>10) | +25 | * | Mersenne | +100 | * | Sophie Germain | +5 | */ function scorePrime( p: number, prevPrime: number | null, gapRecords: Set<number> ): InterestingPrime { let score = 1 const tags: PrimeInterestTag[] = [] // Twin (gap 2) if (isPrime(p + 2) || (p - 2 >= 2 && isPrime(p - 2))) { score += 10 tags.push('twin') } // Cousin (gap 4) if (isPrime(p + 4) || (p - 4 >= 2 && isPrime(p - 4))) { score += 5 tags.push('cousin') } // Sexy (gap 6) if (isPrime(p + 6) || (p - 6 >= 2 && isPrime(p - 6))) { score += 3 tags.push('sexy') } // Prime triplet: (p, p+2, p+6) or (p, p+4, p+6) const isTriplet = (isPrime(p + 2) && isPrime(p + 6)) || (isPrime(p + 4) && isPrime(p + 6)) || (p - 2 >= 2 && isPrime(p - 2) && isPrime(p + 4)) || (p - 4 >= 2 && isPrime(p - 4) && isPrime(p + 2)) || (p - 6 >= 2 && isPrime(p - 6) && isPrime(p - 4)) || (p - 6 >= 2 && isPrime(p - 6) && isPrime(p - 2)) if (isTriplet) { score += 30 tags.push('triplet') } // Prime quadruplet: (p, p+2, p+6, p+8) const isQuad = (isPrime(p + 2) && isPrime(p + 6) && isPrime(p + 8)) || (p - 2 >= 2 && isPrime(p - 2) && isPrime(p + 4) && isPrime(p + 6)) || (p - 6 >= 2 && isPrime(p - 6) && isPrime(p - 4) && isPrime(p + 2)) || (p - 8 >= 2 && isPrime(p - 8) && isPrime(p - 6) && isPrime(p - 2)) if (isQuad) { score += 50 tags.push('quadruplet') } // Palindrome if (isPalindrome(p)) { score += 20 tags.push('palindrome') } // Gap record (from sieve-range cache) if (gapRecords.has(p)) { score += 30 tags.push('gap-record') } // High merit gap: merit = gap / ln(p) > 10 if (prevPrime !== null && p > 2) { const gap = p - prevPrime const merit = gap / Math.log(p) if (merit > 10) { score += 25 tags.push('high-merit') } } // Mersenne prime if (MERSENNE_PRIMES.has(p)) { score += 100 tags.push('mersenne') } // Sophie Germain: 2p+1 is also prime const safePrime = 2 * p + 1 if (safePrime < 1e12 && isPrime(safePrime)) { score += 5 tags.push('sophie-germain') } return { value: p, score, tags } } // --- Density-adaptive threshold --- /** * Compute the score threshold based on prime density (primes per pixel). */ function computeScoreThreshold(primeCount: number, cssWidth: number): number { if (cssWidth <= 0 || primeCount <= 0) return 0 const primesPerPixel = primeCount / cssWidth if (primesPerPixel < 0.05) return 0 // sparse — show all if (primesPerPixel < 0.5) return 15 if (primesPerPixel < 2) return 30 return 50 // extreme density } // --- Main entry point --- /** * Compute interesting primes for the visible range. * * Tier 1 (live): If computeVisiblePrimes returns results, score all of them. * Tier 2 (landmark): Fall back to precomputed landmark table. * * Returns a filtered list based on density-adaptive threshold. */ export function computeInterestingPrimes( leftValue: number, rightValue: number, cssWidth: number ): InterestingPrime[] { const livePrimes = computeVisiblePrimes(leftValue, rightValue) let scored: InterestingPrime[] if (livePrimes.length > 0) { // Tier 1: live scoring const { primes: gapRecords } = ensureGapRecords() scored = [] let prevPrime: number | null = null for (const p of livePrimes) { scored.push(scorePrime(p, prevPrime, gapRecords)) prevPrime = p } } else { // Tier 2: landmark fallback const landmarks = getLandmarksInRange(leftValue, rightValue) scored = landmarks.map((lp: LandmarkPrime) => ({ value: lp.value, score: lp.score, tags: lp.tags, note: lp.note, })) } if (scored.length === 0) return [] // Apply density-adaptive threshold const threshold = computeScoreThreshold(scored.length, cssWidth) if (threshold === 0) return scored return scored.filter((p) => p.score >= threshold) } |