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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.

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**Knewlogik****Member**- Registered: 2020-05-11
- Posts: 19

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

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