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%I #17 Aug 03 2014 14:27:52
%S 1354361,1354343,1354333,1354321,1354307,1354291,1354231,1354207,
%T 1354181,1354153,1354057,1354021,1353983,1353901,1353857,1353763,
%U 1353713,1353607,1353551,1353433,1353371,1353241,1353173,1352957
%N Primes among the absolute value of numbers of the form f(x)= x^2 + x - 1354363.
%C 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].
%D R. Crandall and C. Pomerance, Prime Numbers A Computational Perspective, Springer Verlag 2002, p. 49, exercise 1.17.
%e f(1) = 1+1-1354363 = -1354361. Absolute value of -1354361 = 1354361.
%t Select[Table[Abs[n^2+n-1354363], {n, 0, 100}], PrimeQ] (* _Arkadiusz Wesolowski_, Mar 06 2011 *)
%o (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) }
%K easy,nonn,less
%O 1,1
%A _Cino Hilliard_, Aug 17 2006
%E Offset corrected by _Arkadiusz Wesolowski_, Mar 02 2011
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