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A number theory post

Let p be a prime.

Consider the primes in [1,p(p+1)].

All residue classes a mod p occur in that interval.

Example

P = 5
Interval [1,5*6] = [1,30]

1 mod 5 : 11
2 mod 5 : 2,7,17
3 mod 5 : 3,13,23
4 mod 5 : 19,29

Regards

Tommy1729