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prime number theorem
(redirected from Distribution of prime numbers)

    Also found in: Wikipedia 0.03 sec.
(mathematics)prime number theorem - The number of prime numbers less than x is about x/log(x). Here "is about" means that the ratio of the two things tends to 1 as x tends to infinity. This was first conjectured by Gauss in the early 19th century, and was proved (independently) by Hadamard and de la Vall'ee Poussin in 1896. Their proofs relied on complex analysis, but Erdös and Selberg later found an "elementary" proof.


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Speaking of the distribution of prime numbers, he says: "A somewhat better approximation is LogIntegral[n], equal to Integrate[1/Log[t],{t,2,n}].
Not Quite Copernicus by DERBYSHIRE, JOHN / National Review
To gain insights into the somewhat irregular distribution of prime numbers, mathematicians have studied a variety of subsets of all primes.
The scarcity of cluster primes by I.P. / Science News
The discovery of such a large Mersenne prime by a hit-or-miss approach actually has little value for computational number theorists interested in the distribution of prime numbers and related mathematical issues.
Striking pay dirt in prime-number terrain by Peterson, Ivars / Science News
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