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.
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
KEYWORD
easy,nonn,less
AUTHOR
Cino Hilliard, Aug 17 2006
EXTENSIONS
Offset corrected by Arkadiusz Wesolowski, Mar 02 2011
STATUS
approved