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Search: id:A130916
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| A130916 |
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Number of primes between n^2 and n^3. |
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+0
1
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| 0, 0, 2, 5, 12, 21, 36, 53, 79, 107, 143, 187, 235, 288, 356, 428, 510, 595, 699, 810, 929, 1062, 1206, 1358, 1528, 1707, 1898, 2098, 2323, 2561, 2807, 3066, 3340, 3636, 3946, 4283, 4611, 4975, 5351, 5755, 6162, 6587, 7034, 7506, 7998, 8504, 9042, 9587, 10157
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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There is always a prime between n^2 and n^3 for n > 1. For n = 2, primes 5 and 7 are between 4 and 8. For n > 2, we have the number of primes between n^2 and n^3 ~ n^3/log(n^3) - n^2/log(n^2) = n^2(2n-3)/(6log(n)) -> infinity as n -> infinity. A corollary to this is the number of primes are infinite.
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PROGRAM
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(PARI) /* Count primes between x^2 and x^3. */ primex2x3(m, n) = { local(x, y, c); for(x=m, n, c=0; for(y=x^2, x^3, if(ispseudoprime(y), c++) ); print(c) ) }
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CROSSREFS
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Sequence in context: A116728 A095306 A079648 this_sequence A080838 A106331 A116727
Adjacent sequences: A130913 A130914 A130915 this_sequence A130917 A130918 A130919
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard (Hillcino368(AT)hotmail.com), Aug 23 2007
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