Prime Numbers

Rule, exact count and rarity

A prime is an integer greater than 1 with exactly two positive divisors, 1 and itself. Neither 0 nor 1 is prime. The only even prime is 2; larger even integers have 2 as a proper divisor. RNGDLE.ART identifies primes through factorization, and the dataset counts each integer once rather than estimating frequency with a prime-number approximation. A prime can simultaneously have decimal or binary digit patterns, which may make some primes rank much higher than others. Primality itself does not depend on the base used to write an integer, whereas a palindrome or repeated-digit appearance does. The pattern's frequency is evaluated only within this finite inclusive range and should not be presented as a probability over all integers.

The exact count, 78,498, comes from evaluating all 1,000,001 integers from 0 through 1,000,000, including both endpoints. It is not a sample or an estimate. Each matching integer is counted once for this category, even if it contains multiple qualifying segments. Its frequency of 7.849792% describes the chance that a uniformly chosen integer passes this one test. It is not the global score percentile of every member, and overlapping pattern counts must not be added as if they represented disjoint sets.

The pattern supplies −log₂(78,498 / 1,000,001) bits before its within-family weight is applied. Other matched patterns, digit sum, distinct-digit count and short-length signals can change the complete score. Consequently, members of this category need not share a ranking. The highest-scoring representative is 3, with a rarity score of 1,677 and Top 0.0001%. This uses its complete score across all features, not just this pattern. Equal scores are displayed in ascending numerical order.

Example numbers

The highest-scoring match

The highest-scoring representative is 3, with a rarity score of 1,677 and Top 0.0001%. This uses its complete score across all features, not just this pattern. Equal scores are displayed in ascending numerical order.