Try f_2=1.260997000000
k p_k f_k time ln k+lnln k-(f_k/k)^.5
2 3 1.260997 0 -0.467405
3 5 3.00788726543 0 0.191346
4 7 5.86093616488 0 0.502460
5 11 9.03207826012 0 0.741293
6 13 13.3034371748 0 0.885918
7 17 17.9968693037 0 1.008212
8 19 23.9097203956 0 1.082751
9 23 30.3872024218 0 1.146933
10 29 36.7236984479 0 1.220275
21 73 138.877079812 0 1.586253
100 541 1691.36119643 0 2.019734
1000 7919 42420.1943523 0 2.327321
10000 104729 802070.328172 0 2.474829
51000 625187 5820352.04126 0 2.539876
100000 1299709 12982769.6023 0 2.562200
1000000 15485863 190542531.476 0 2.637588
10000000 179424673 2582959035.71 2 2.826451
Succeeded at k=21381000, p=400885651
5 seconds
Try f_2=1.260997375000
k p_k f_k time ln k+lnln k-(f_k/k)^.5
2 3 1.260997375 0 -0.467405
3 5 3.00788829491 0 0.191346
4 7 5.86093846316 0 0.502460
5 11 9.03208215279 0 0.741293
6 13 13.3034434829 0 0.885917
7 17 17.9968785286 0 1.008212
8 19 23.9097336708 0 1.082750
9 23 30.3872205162 0 1.146933
10 29 36.7237215536 0 1.220274
21 73 138.87721517 0 1.586252
100 541 1691.36577667 0 2.019728
1000 7919 42420.7843378 0 2.327276
10000 104729 802133.77222 0 2.474475
51000 625187 5821999.05463 0 2.538365
100000 1299709 12989046.9042 0 2.559446
1000000 15485863 191137675.865 0 2.616047
10000000 179424673 2637430663.15 2 2.657870
100000000 2038074743 34752192543.7 24 2.692215
1000000000 22801763489 441872868631 276 2.733751
10000000000 252097800623 5.42093223619e+012 3250 2.879573
Succeeded at k=19269602000, p=498961938779
6523 seconds