Rarity Methodology
Every rarity score on RNGdle.net is calculated from a complete analysis of all 1,000,001 supported numbers (0 to 1,000,000). Nothing is estimated or sampled.
Supported range and representation
The supported range is 0 to 1,000,000 inclusive. Numbers are analyzed by their natural decimal representation with no leading zeros, so 7 is treated as a one-digit number, not "000007". Digit-based traits (length, palindrome, sequences) follow directly from that representation.
Step 1 — Extract features
Each number is reduced to a set of boolean traits plus two distribution features (digit sum and count of distinct digits). Traits are organized into groups so correlated properties can be de-duplicated later.
Step 2 — Exact probability and information
For each trait f, we count how many of the 1,000,001 numbers
match it. The probability is count / 1,000,001 and its
information content is -log2(probability). Rarer traits carry more bits and
contribute more to the score. Below are the exact counts used by the current algorithm.
| Trait | Group | Matches | Probability |
|---|---|---|---|
| Single-digit number | range | 10 | 1 in 100,000 |
| Two-digit number | range | 90 | 1 in 11,111 |
| Three-digit number | range | 900 | 1 in 1,111 |
| Four-digit number | range | 9,000 | 1 in 111 |
| All digits identical | repetition | 45 | 1 in 22,222 |
| Five or more of one digit | repetition | 487 | 1 in 2,053 |
| Quadruple digit | repetition | 11,340 | 1.13% |
| Triple digit | repetition | 138,024 | 13.80% |
| Double pair | repetition | 223,803 | 22.38% |
| Repeated digit | repetition | 457,731 | 45.77% |
| Adjacent digit run | repetition | 35,884 | 3.59% |
| Only two distinct digits | repetition | 4,294 | 1 in 233 |
| Palindrome | symmetry | 1,989 | 1 in 503 |
| Sequential ascending | sequence | 22 | 1 in 45,455 |
| Sequential descending | sequence | 26 | 1 in 38,462 |
| Ascending segment | sequence | 28,826 | 2.88% |
| Descending segment | sequence | 29,815 | 2.98% |
| ABAB pattern | sequence | 243 | 1 in 4,115 |
| ABCABC pattern | sequence | 891 | 1 in 1,122 |
| Alternating parity | sequence | 34,875 | 3.49% |
| Harshad number | arithmetic | 95,428 | 9.54% |
| Happy number | arithmetic | 143,071 | 14.31% |
| Prime | factorization | 78,498 | 7.85% |
| Semiprime | factorization | 210,035 | 21.00% |
| Perfect square | factorization | 1,001 | 1 in 999 |
| Perfect cube | factorization | 101 | 1 in 9,901 |
| Power of two | factorization | 20 | 1 in 50,000 |
| Fibonacci number | factorization | 30 | 1 in 33,333 |
| Triangular number | factorization | 1,414 | 1 in 707 |
| Factorial | factorization | 9 | 1 in 111,111 |
| Highly divisible | factorization | 2,809 | 1 in 356 |
| Binary palindrome | representation | 1,998 | 1 in 501 |
| All ones in binary | representation | 18 | 1 in 55,556 |
| Hex repdigit | representation | 59 | 1 in 16,949 |
Step 3 — Avoid double counting
Some traits are highly correlated — "all digits identical", "quadruple digit" and "repeated digit" overlap heavily. Traits are grouped into range, repetition, symmetry, sequence, arithmetic, factorization, representation. Within each group only the strongest trait scores in full; the rest are attenuated by decreasing weights (1, 0.35, 0.15, 0.07, 0.03) so a family of related traits cannot stack indefinitely.
Step 4 — Score to percentile
Group contributions are summed into total bits and scaled to an integer rarity score. Because every number was scored during the build, we know the exact score distribution and can map any score to a precise percentile. The current build has a maximum score of 1,677 across 803 distinct score values.
| Tier | Percentile | Minimum score |
|---|---|---|
| Singular | Top 0.1% | 600 |
| Extreme | Top 1% | 391 |
| Exceptional | Top 5% | 298 |
| Rare | Top 10% | 259 |
| Distinct | Top 25% | 207 |
| Notable | Top 50% | 166 |
Step 5 — Versioning
The scoring configuration is versioned. Every result records the algorithm version it was produced with, so a shared number keeps its meaning even after the algorithm is updated.
Current algorithm version: 1.0.0 · Built 2026-07-28
Cultural features
Meme numbers, year-like numbers and date-like numbers are interesting but subjective, so they are intentionally kept out of the mathematical rarity score. If added later, they will be shown separately and clearly labelled.