Compute number of primes of form x^2 + x + A for x <= 10^11 (for Jacobson and Williams A = 3399714628553118047)

a11.3399714628553118047.gp

export(A=3399714628553118047); a(n)=parsum(k=0, 10^n, isprime(k^2+k+A));
default(threadsizemax,1000*10^6);                \\ default 8MB was too small
#
print(a(11));

Michael J. Jacobson, Jr.,
Computational techniques in quadratic fields,
Master’s thesis, University of Manitoba, Winnipeg, Manitoba, 1995.

Michael J. Jacobson Jr. and Hugh C. Williams,
New Quadratic Polynomials With High Densities Of Prime Values,
Math. Comp., 72, 241, 499-519, 2002.

Number of primes of the form x^2 + x + A for x <= 10^n, with A=3399714628553118047 from Jacobson:

 n        a(n)
-- -----------
 0           1
 1           5
 2          24
 3         235
 4        2482
 5       25034
 6      251841
 7     2517022
 8    25153819
 9   251014697
10  2408242218
11 22066543923

a(11) is 1.61412× bigger than a(11) for A=41 (Euler polynomial primes),
and 5.35848× bigger than number of "normal" primes up to 10¹¹.