Finding prime pairs with particular gaps

Cutter, Pamela A.

doi:10.1090/s0025-5718-01-01327-8

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2004

2024

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Cited by 3 publications

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Prime Numbers

Guy

2004

Problem Books in Mathematics

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A number greater than 1 is prime if its only positive divisors are 1 and itself; otherwise it's composite. Primes have interested mathematicians at least since Euclid, who showed that there are infinitely many. The largest prime in the Bible is 22273 at Numbers, 3 xliii.The greatest common divisor (gcd) of m and n is denoted by (m, n), e.g., (36,66) = 6, (14,15) = 1, (1001,1078) = 77. If (m, n) = 1, we say that m and n are coprime and write m ..1 n; for example 182 ..1 165.Denote the n-th prime by Pn, e.g. PI = 2, P2 = 3, P99 = 523; and the number of primes not greater than x by 7r(x), e.g., 7r(2) = 1, 7r(3~) = 2, 7r(1000) = 168, 7r(4· 10 16 ) = 1075292778753150.

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