Twin, cousin, and sexy prime counting function. Explicit formulas
DOI:
https://doi.org/10.3842/umzh.v76i8.7567Keywords:
prime numbers, twin prime numbers, cousin prime numbers, sexy prime numbers, counting function.Abstract
UDC 511
We give explicit formulas for the twin-prime and cousin-prime counting functions. We propose a formula that computes the number of primes less than or equal to $n$ whose difference is $m\geqslant 6.$ We also present a characterization specifying when two numbers whose difference is $n\geqslant 2$ are primes.
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