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 ⩾ 6. We also present a characterization specifying when two numbers whose difference is n ⩾ 2 are primes.
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Krzysztof Kowitz (2024) studied this question.
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