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Should be able to trivially extend that logic to Mersenne Primes then, 'presumably'
by Jerrrrrrry 2y ago
Should be able to trivially extend that logic to Mersenne Primes then, 'presumably'
- NeoTar 2y agoIt’s not. The traditional proof that there are an infinite number of primes relies on unique prime factorisation- i.e for any number, n, there is a unique set of primes p1, p2, p3, … etc. where p1 * p2 * p3 * … = n For instance 88 = 2 * 2 * 2 * 11, 42 = 2 * 3 * 7 It’s worth reading the proof if you haven’t - it’s comprehensible with high school maths. No such property exists for Mersenne primes, so we can’t trivially extend it. Many proofs of the properties of prime numbers are difficult because they, by definition, actively resist patterns.
- af3d 2y agoYes, the Mersenne primes do indeed extend to infinity. That is due to the simple fact that perfect numbers (for which they are intimately connected to) are also known to be infinite in number.
- Jerrrrrrry 2y agoThis was an instant deduction, thank you. I tried some flavors of primes but you'd think the most intuitive one by a magnitude would be listed on the Wiki for proofs.