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http://www.novaspivack.com/science/we-have-discovered-a-new-pattern-in-the-prime-numbers-parallax-compression

A lot of cryptographic algorithms depends on prime numbers.

Will this influence any cryptographic algorithms?

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I think poncho's comment sums it perfectly:

No.

As for the why (because SE won't let me post just the above as an answer), the result (if it is new), only makes a statement about the distribution of primes. But first we already know enough about their distribution that we can say that there are enough in the ranges relevant to cryptography and we're only using primes anyways for parameters or maybe for keys and there the distribution only influences the time it takes to come up with a good / valid key or parameter. But then key generation / parameter generation tends to be an operation that only happens relatively rarely anyways...

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