Is there any pattern in prime numbers

Question

Do a pattern exist in set of prime numbers or is there any expression for a prime number?? I am unable to find any relation between prime numbers

Depends what you mean by a "pattern". As for "expression for a prime number", see e.g. Formula for primes — Robert Israel, May 12 '17 at 18:42

score 3 · Accepted Answer · answered May 12 '17 at 18:26

3

Hint -

All primes greater than 3 should be in the form $6k \pm 1$.

Hope now you are able to find pattern.

answered May 12 '17 at 18:26

Kanwaljit Singh

I to found the same ans in a book but could not found its derivation, can it be proved?, – vishesh das May 12 '17 at 18:32
@vish Yes it can be proved. $6k\pm 1$ is the same as $6k + 1 \cup (6k - 1=6k+5)$. That leaves 4 other cases: $6k+0, 6k+2, 6k+3, 6k+4$. Each of those four cases is divisible by 2 or 3. Also note, that not all number of the form $6k\pm 1$ are prime. Rather all primes are of that form. Finally, another, a slightly more selective pattern is all primes are $\equiv \mod 30$ one of the following: $1,7,11,13,17,19,23,29$. You can also come up with a similar, but more refined list $\equiv \mod 210$ – Χpẘ May 12 '17 at 18:59

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