I’ve read books about prime numbers and I did not know this.
Comment on What are the most mindblowing fact in mathematics?
backseat@lemmy.world 11 months ago
The square of any prime number >3 is one greater than an exact multiple of 24.
For example, 7² = 49= (2 * 24) + 1
Pulptastic@midwest.social 11 months ago
Thoth19@lemmy.world 11 months ago
Does this really hold for higher values? It seems like a pretty good way of searching for primes esp when combined with other approaches.
metiulekm@sh.itjust.works 11 months ago
Every prime larger than 3 is either of form 6k+1, or 6k+5; the other four possibilities are either divisible by 2 or by 3 (or by both). Now (6k+1)² − 1 = 6k(6k+2) = 12k(3k+1) and at least one of k and 3k+1 must be even. Also (6k+5)² − 1 = (6k+4)(6k+6) = 12(3k+2)(k+1) and at least one of 3k+2 and k+1 must be even.