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% |
| Zigzag digits | sequence | 136,425 | 13.64% |
| 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 |
Distribution features
Digit sum and distinct-digit count are scored from their exact distributions across the supported range. Daily game trait links such as “Digit sum 23” point here because these values vary by number rather than belonging to one fixed boolean-trait row above.
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 807 distinct score values.
| Tier | Percentile | Minimum score |
|---|---|---|
| Singular | Top 0.1% | 603 |
| Extreme | Top 1% | 399 |
| Exceptional | Top 5% | 303 |
| Rare | Top 10% | 266 |
| Distinct | Top 25% | 218 |
| Notable | Top 50% | 175 |
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: 1.1.0 · Built 2026-09-06
A known limitation — length
Only ten of the 1,000,001 supported numbers have a single digit, so "is a single-digit number" carries about as much information as a strong pattern, and the score treats it that way. Short numbers also have very few distinct digits and very small digit sums, which are rare in their own right. The result is that short numbers dominate any raw ranking: sixty-five of the hundred highest-scoring numbers in the range have three digits or fewer.
This is measured correctly and is not adjusted away — but it is worth being clear about what it measures. Length is not a property of a number, it is a property of where the range was cut off. Widen the range to ten million and 3 would score higher still, while 3,003 would not move. Everything else the score counts — palindromes, factorisations, digit patterns — is intrinsic to the number and does not depend on the boundary.
Individual scores are left untouched, so a short number's page reports exactly what the algorithm computed. Where a ranking is presented, though, the boards start at four digits, because otherwise they would rank the boundary rather than the numbers — see the leaderboard and the examples on the pattern pages.
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.