Every answer takes you to the table. Pick a question:
Every prime greater than 5 ends in 1, 3, 7, or 9. The primes 2 and 5 are the only exceptions — the only ones ending in their respective digits. Showing all 168 primes up to 1000.
Click a card to highlight every matching prime in the table above.
Primes p where p+2 or p−2 is also prime — pairs like (3,5), (11,13), (17,19), (29,31).
Primes p where 2p+1 is also prime. Key in number theory and cryptography.
Primes that read the same forwards and backwards (excluding single digits).
Primes of the form 4k+1. By Fermat’s theorem, exactly these are expressible as a sum of two squares.
Primes p where 2ᵖ − 1 is also prime — the exponents of Mersenne primes.
Foundational facts that govern the distribution of prime numbers.
Euclid’s proof: suppose only finitely many primes p₁, p₂, …, pₙ. Then N = p₁ p₂ ⋯ pₙ + 1 isn’t divisible by any of them, so either N is prime or has a new prime divisor. Either way, a contradiction.
π(n), the count of primes ≤ n, grows like n/ln(n). The 25 highlighted cells below are the primes under 100 — 25% density that thins out as n grows.
π(100)=25, π(1000)=168, π(10000)=1229Every prime greater than 5 ends in 1, 3, 7, or 9. Numbers ending in 0, 2, 4, 5, 6, or 8 are composite (with 2 and 5 themselves as the only exceptions).
127, 131, 137, 139 — four consecutive valid endingsA prime p > 2 can be written as a² + b² for positive integers a, b iff p ≡ 1 (mod 4). Fermat’s theorem on sums of two squares.
5 = 1² + 2² · 13 = 2² + 3² · 29 = 2² + 5²