Computed with engine art-1.0.0. Data updated: 2026-09-26 (UTC). Rules independently implemented by RNGDLE.ART.
Number theory
Rule, exact count and rarity
A factorial value is the product of the positive integers from 1 through k. Both 0! and 1! equal 1, and the atlas counts that integer only once. Zero itself is not a factorial value. Repeated multiplication makes factorials grow very quickly, so only a small finite list stays inside this calculator's range. Factorial membership is different from being divisible by a factorial: many multiples of 24 are not themselves factorial values. The engine builds the set of actual products up to the maximum and checks for exact membership. Factorials often have several other arithmetic properties, but shared factorization signals receive the usual within-family discounts when the full rarity score is assembled.
The exact count, 9, 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 0.0009% 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(9 / 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 1, with a rarity score of 1,504 and Top 0.0002%. This uses its complete score across all features, not just this pattern. Equal scores are displayed in ascending numerical order.
Example numbers
ExploreThe highest-scoring match
The highest-scoring representative is 1, with a rarity score of 1,504 and Top 0.0002%. This uses its complete score across all features, not just this pattern. Equal scores are displayed in ascending numerical order.
Frequently asked questions
How many factorial numbers are there between 0 and 1,000,000?
There are exactly 9 matches for factorial numbers among the 1,000,001 integers from 0 to 1,000,000, inclusive: 0.0009% of the range. A product 1 × 2 × … × k, including 1.
Do 0! and 1! create two factorial matches?
No. Both equal the integer 1, which is counted once. Zero is not itself a factorial value.
What is the highest-scoring factorial numbers representative?
The highest-scoring representative is 1, with a rarity score of 1,504 and Top 0.0002%. This uses its complete score across all features, not just this pattern. Equal scores are displayed in ascending numerical order.