Which proof is harder: the Rieman conjecture or the fact that there are infinitely many prime numbers?
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The phrase “There are infinitely many prime numbers” is very easy to prove, the basic features of the evidence are already in school.
The Riemannian presumption has not yet been proven by anyone, this is probably more difficult (but maybe someone comes around at some point with a very simple proof, who knows…).
Or this assumption belongs to a class of assumptions that cannot be proven at all. After all, you’ve been looking for evidence for over 160 years. This is for me the unsatisfactory thing about mathematics, that there are also invincibles. You don’t find proof, but you don’t find a counter-example. Simple gray zone. But who knows…
This is also possible. Yes, incompleteness hurts.
I’m guessing the Riemannian PROTECTION… 🙂
🙂
That there are infinite numbers of primes is amazingly easy to prove; here:
Annahne: There are many prime numbers, we call the times p_1…p_n. Then the numbers m=1 + p_1 * p_2 * … * p_n. This number has the remainder 1 in the division with all (finally many) prime numbers, i.e. it can be divided by none of the prime numbers p_1…p_n. Thus, m is either a prime number itself, or m can be divided by a prime number which is greater than al p_n. This is contrary to the assumption that p_n is the largest prime number, i.e. the assumption that there are only at last many prime numbers, was wrong, i.e. there are infinite numbers of primes.
The Riemannian presumption is definitely more difficult to prove!