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A120609 Primes among the absolute value of numbers of the form f(x)= x^2 + x - 1354363. 0
1354361, 1354343, 1354333, 1354321, 1354307, 1354291, 1354231, 1354207, 1354181, 1354153, 1354057, 1354021, 1353983, 1353901, 1353857, 1353763, 1353713, 1353607, 1353551, 1353433, 1353371, 1353241, 1353173, 1352957 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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].
REFERENCES
R. Crandall and C. Pomerance, Prime Numbers A Computational Perspective, Springer Verlag 2002, p. 49, exercise 1.17.
LINKS
EXAMPLE
f(1) = 1+1-1354363 = -1354361. Absolute value of -1354361 = 1354361.
MATHEMATICA
Select[Table[Abs[n^2+n-1354363], {n, 0, 100}], PrimeQ] (* Arkadiusz Wesolowski, Mar 06 2011 *)
PROG
(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) }
CROSSREFS
Sequence in context: A067516 A184661 A187961 * A094914 A138027 A222155
KEYWORD
easy,nonn,less
AUTHOR
Cino Hilliard, Aug 17 2006
EXTENSIONS
Offset corrected by Arkadiusz Wesolowski, Mar 02 2011
STATUS
approved

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Last modified June 14 23:20 EDT 2024. Contains 373401 sequences. (Running on oeis4.)