Find all $p$ is prime number such that Both $p+14$ and $p+20$ are Prime number.

Asked Nov 19 '20 at 08:47

Active Nov 19 '20 at 09:00

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Find all $p$ is prime number such that Both $p+14$ and $p+20$ are Prime number. I knomw $p=3,p=17,p=23$, but I can't to show that is that all.

asked Nov 19 '20 at 08:47

Hung nguyen

1

I doubt that there is a finite number of them. Type x=1;x=x+1;x<10000;x;isprime(x) and isprime(x+14) and isprime(x+20) into https://www.alpertron.com.ar/ECM.HTM to get all primes under 10000 satisfying this condition. – player3236 Nov 19 '20 at 09:00
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The (generalized) Bunyakovsky conjecture predicts infinite many such primes , but it is open whether this is actually the case. – Peter Nov 19 '20 at 09:07
A large example is $$10^{100}+1890007$$ – Peter Nov 19 '20 at 09:11

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