Published: · Updated:
Computed with engine art-1.0.0. Data updated: 2026-09-26 (UTC). Rules independently implemented by RNGDLE.ART.
- 01
We examine every integer from 0 through 1,000,000, written without leading zeros. Each pattern's probability is its exact match count divided by 1,000,001. The table includes every one of the 31 patterns.
- 02
Information is −log₂(probability). Digit sum and distinct-digit count also supply information from their exact distributions; lengths of one to four digits form a separate group. The score is a defined feature-information measure, not a joint probability computed from independent events.
- 03
Within each family, signals are sorted by information and weighted 1, 0.35, 0.15, 0.07 and 0.03. The sixth and later signals have zero weight. All weighted information is added, multiplied by 20 and rounded once. Individually rounded displayed contributions can differ slightly from the final total.
- 04
Top % = the count of integers scoring at least as high ÷ 1,000,001 × 100. All tied scores are included, and a smaller value means a higher rarity ranking. Top 1% means about 1% of integers reach or exceed that score. It is an upper-tail percentage, not the first percentile or an interchangeable label for the 99th percentile.
- 05
Short numbers often score highly because they are scarce in this fixed range. The existing highest and lowest leaderboards display only 1,000 through 1,000,000; the rarest-numbers ranking covers the whole range from 0 through 1,000,000. Both use the same full-range frequencies and Top %; their displayed candidate ranges differ.
Engine version: art-1.0.0. All counts are generated from this project’s independently implemented rules. Individual rounded contributions may not sum to the final score.
Exact statistics for all 31 patterns
| Pattern | Frequency | matches |
|---|---|---|
| Repdigit number | 0.004% | 45 |
| At least five repeated digits | 0.049% | 487 |
| Exactly four repeated digits | 1.134% | 11,340 |
| Exactly three repeated digits | 13.802% | 138,024 |
| Multiple digit pairs | 22.38% | 223,803 |
| Exactly one digit pair | 45.773% | 457,731 |
| Consecutive repeated digits | 3.588% | 35,884 |
| Exactly two distinct digits | 0.429% | 4,294 |
| Palindrome number | 0.199% | 1,989 |
| Consecutive ascending digits | 0.002% | 22 |
| Consecutive descending digits | 0.003% | 26 |
| Ascending segment | 2.883% | 28,826 |
| Descending segment | 2.981% | 29,815 |
| ABAB pattern | 0.024% | 243 |
| ABCABC pattern | 0.089% | 891 |
| Alternating parity | 3.487% | 34,875 |
| Zigzag digits | 13.642% | 136,425 |
| Harshad number | 9.543% | 95,428 |
| Happy number | 14.307% | 143,071 |
| Prime number | 7.85% | 78,498 |
| Semiprime | 21.003% | 210,035 |
| Perfect square | 0.1% | 1,001 |
| Perfect cube | 0.01% | 101 |
| Power of two | 0.002% | 20 |
| Fibonacci number | 0.003% | 30 |
| Triangular number | 0.141% | 1,414 |
| Factorial | 0.001% | 9 |
| At least 100 positive divisors | 0.281% | 2,809 |
| Binary palindrome | 0.2% | 1,998 |
| Mersenne number (binary repunit) | 0.002% | 18 |
| Hexadecimal repdigit | 0.006% | 59 |
Frequently asked questions
How is the RNGDLE rarity score calculated?
Each signal contributes −log₂(match count / 1,000,001). Patterns, digit sum, distinct-digit count and lengths of one to four digits use their respective distributions. Within each family, signals are sorted by information and weighted 1, 0.35, 0.15, 0.07 and 0.03; later weights are zero. The weighted total is multiplied by 20 and rounded once.
What does the percentile or Top % mean?
Top % is the percentage of all 1,000,001 integers whose score is at least as high as yours, including ties. Smaller is rarer. Top 1% means about 1% reach or exceed that score; it does not mean the first percentile.
Are the pattern statistics sampled or exhaustive?
All 31 counts are exact results of evaluating every integer from 0 through 1,000,000, a total of 1,000,001 values. Several patterns can match the same integer.