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));

Started on 192C/384T Lenovo x3950-X6 8-socket server with Intel Xeon 8890v4 CPUs with

nohup numactl -C 0-191 gp -q < a11.3399714628553118047.gp 

this was longest such computation for x≤10¹¹ sequences mostly from oeis.org sofar.
a(11)=22066543923 was computed in 27:10h real time, and 215.55 days total time:

hermann@x3950-X6:~$ cat nohup.out
   timer = 1 (on)
22066543923
cpu time = 5215h, 10min, 39,011 ms, real time = 27h, 10min, 3,006 ms.
hermann@x3950-X6:~$ 

hermann@x3950-X6:~$ stat nohup.out
  File: nohup.out
  Size: 122       	Blocks: 8          IO Block: 4096   regular file
Device: 8,2	Inode: 144770244   Links: 1
Access: (0600/-rw-------)  Uid: ( 1000/ hermann)   Gid: ( 1000/ hermann)
Access: 2026-01-17 00:52:24.273924746 +0100
Modify: 2026-01-16 23:14:07.194919374 +0100
Change: 2026-01-16 23:14:07.194919374 +0100
 Birth: 2026-01-15 20:04:03.993695686 +0100
hermann@x3950-X6:~$ 

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.