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I had a question about these prime number announcements you hear now and again. When there's a new "largest prime" announced, does that mean we know all the pr
by lordnacho 2y ago
I had a question about these prime number announcements you hear now and again.
When there's a new "largest prime" announced, does that mean we know all the primes below that number?
- bloak 2y agoNo. The "largest prime" announcements generally refer to a Mersenne prime, which is one that is one less than a power of two. There is a faster primality test for such numbers.
- ndsipa_pomu 2y agoNo - it's common to try to find large Mersenne Primes (https://en.wikipedia.org/wiki/Mersenne_prime https://en.wikipedia.org/wiki/Mersenne_prime) which are primes that are one less than a power of 2. This will miss out a lot of non-Mersenne primes.
- cbm-vic-20 2y agoCorollary: given two numbers a and b, is it possible to prove there are no prime numbers between them? (ie, does there exist a prime p such that a < p < b ?)