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zetafunc

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Registered: 2014-05-21

Posts: 2,436

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Re: All primes formula

If

denote the prime numbers, then there exists a constant

and a sequence

such that

is the nth prime. It can be shown that this recurrence relation generates all the prime numbers -- however, the complexity of this problem (as is often the case with prime-generating constants) is determining the value of

to a sufficiently high degree of accuracy. The proof of this result uses Bertrand's postulate.

Here, I've used

to denote the floor of x (you can think of that as 'rounding down x to the nearest whole number') and

to denote the fractional part of x. So in other words, we'd have

and

.

The exact value of

can be represented as an infinite sum:

You need about 25 terms in the series above to get all the primes less than 100, for example.

Knewlogik

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Registered: 2020-05-11

Posts: 24

Re: All primes formula

Is it safe to say except for 3 13 23 you will never have three consecutive possible primes in a row meaning like three in a row that end in 3 like that showed above our 7 17  27 we took 1 3 7 and 9 and every possible number to Indian in it you will never have three in a row correct that end in it meaning the same number weatherby one three times seven three times but consecutive is that safe to say