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A120609
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Primes among the absolute value of numbers of the form f(x)= x^2 + x - 1354363.
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0
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1354361, 1354343, 1354333, 1354321, 1354307, 1354291, 1354231, 1354207, 1354181, 1354153, 1354057, 1354021, 1353983, 1353901, 1353857, 1353763, 1353713, 1353607, 1353551, 1353433, 1353371, 1353241, 1353173, 1352957
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OFFSET
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1,1
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COMMENTS
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The number of primes of this form for x <= 10000 is 5356. So the probability that a random 0 < x <= 10000 produces a prime in abs(f(x)) is greater than 1/2. The authors in the reference cite an amusing implication. "If you can remember a phone number 1354363, then you have a mental mnemonic for generating thousands of primes." The authors also note that the polynomial f(x) = x^2 + x - 1354363, was found by [Dress and Oliver 1999].
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REFERENCES
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R. Crandall and C. Pomerance, Prime Numbers A Computational Perspective, Springer Verlag 2002, p. 49, exercise 1.17.
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LINKS
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EXAMPLE
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f(1) = 1+1-1354363 = -1354361. Absolute value of -1354361 = 1354361.
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MATHEMATICA
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PROG
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(PARI) g(n) = { c=0; for(x=0, n, y=abs(x^2 + x - 1354363); if(isprime(y), c++; print1(y", "))); print(c", "c/n+.0) }
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CROSSREFS
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KEYWORD
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easy,nonn,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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