Patterns /Number Theory
Prime Numbers
A prime has no divisors other than 1 and itself. They are the building blocks every other number is assembled from.
How long might prime numbers take?
1 in 12.7 per roll · 13 rolls on average.
At one daily specimen a day, the mean is about 0 years. A 50% chance takes 9 rolls; 90% takes 29.
7 daily rolls
43.57%
30 daily rolls
91.39%
365 daily rolls
100.00%
91.39% chance of at least one match in 30 independent rolls.
Waiting times are averages, not deadlines. Previous misses do not increase the next roll’s chance. Only Daily Specimens stamp your Atlas.
Primes thin out as numbers grow, but slowly: the prime number theorem says the density near a number n is about 1 / ln n, so even at a million roughly one number in fourteen is still prime. The exact count is shown above.
That relative abundance is why being prime, on its own, is a modest rarity claim on RNGdle. It is the combination of primality with digit structure that pushes a number up the tiers.
Primality also rules other traits out. A prime above 2 cannot be a semiprime, a perfect square, a perfect cube, or highly divisible — which is why prime numbers rarely dominate the leaderboard.
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
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.
Fibonacci Numbers
Each Fibonacci number is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13 … reaching 832040 before the range runs out.