New Result
 

Hi,

I just finished 2,1294L. 2,737+ is sieving.

2,1294L C187 = p69.p118

p69 = 731712466489221534367281975421345536474565953377641910446355832301081
p118 = 5520892726037575422778927443566198575488546233712998751593111884607229698680175849210737811254045543786744722800872261

Note that

p69 - 1 = 2^3.3.5.7.647.1346346630030951524190921423826719541610668200076620870034510621

and

p69 + 1 = 2.365856233244610767183640987710672768237282976688820955223177916150541

Now if there were a factorization ehnhancement to the p+-1 methods which made the factorization effort dependent on the penultimate factor of p+-1 (rather than the largest factor), that p69 could have been found sans NFS. Hey, a boy can dream, can't he? :wink: