Semiprime Numbers

Rule, exact count and rarity

A semiprime is a product of two prime numbers, allowing the two factors to be equal. The relevant count includes multiplicity: 4 = 2 × 2 qualifies just as 6 = 2 × 3 does. By contrast, 8 has three prime factors when multiplicity is counted and does not qualify, even though it has only one distinct prime factor. The engine uses the total number of prime factors from a complete factorization to apply this rule. Prime squares are therefore both semiprimes and perfect squares. Those overlapping factorization signals are discounted within their shared scoring family. This property describes the integer itself rather than its decimal spelling, so changing the display base does not change whether the number is semiprime.

The exact count, 210,035, 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 21.003479% 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(210,035 / 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 55, with a rarity score of 1,377 and Top 0.0006%. 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 55, with a rarity score of 1,377 and Top 0.0006%. This uses its complete score across all features, not just this pattern. Equal scores are displayed in ascending numerical order.