Patterns /Number Theory
Factorial Numbers
A factorial multiplies together every whole number up to k: 5! = 120, 7! = 5040, 9! = 362880. The next one after that already overshoots a million.
Factorials grow faster than any exponential, so the range holds only a single-digit number of them — the count above is the smallest on the entire site. Hitting one at random is close to impossible.
Every factorial from 3! upward is highly composite by construction, since it is built from all the small primes at once. That means factorials almost always pick up divisor-count traits as well.
If the Infinite Roll simulator ever lands on one, it is worth a screenshot. The probability simulator will tell you just how long a wait that typically is.
Highest-scoring examples
The best-scoring numbers of four digits or more that carry this pattern. Shorter numbers are excluded here because their length alone dominates any score ranking.
Smallest examples
The first numbers in the range that match this pattern.
Related number theory patterns
Prime Numbers
A prime has no divisors other than 1 and itself. They are the building blocks every other number is assembled from.
Semiprime Numbers
A semiprime is a product of exactly two primes, counted with multiplicity — 15 = 3 × 5, and 49 = 7 × 7 counts too.
Perfect Squares
A perfect square is some whole number times itself: 144 = 12², 10000 = 100². The range ends neatly on 1,000,000 = 1000².
Perfect Cubes
A perfect cube is a whole number raised to the third power: 216 = 6³, 970299 = 99³. There are only about a hundred in the entire range.
Powers of Two
Each power of two is double the last: 1, 2, 4, 8, 16, and on up through 1024, 65536 and 524288. Doubling exhausts the range in only twenty steps.