

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+11354363 = 1354361. Absolute value of 1354361 = 1354361.


MATHEMATICA



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



EXTENSIONS



STATUS

approved



