740856 is at index 5824; this is one of the longer sequences now, though it's afflicted with 2^4*31
746564 at 100 digits, 2^4*3^2*5

Reserving 749320, 749640

[QUOTE=Batalov;200249]Done with 745948 746112 747456 747726 749304 749328 749952
Reserving 746712 746856 746880 746886 747120 747720 747762[/QUOTE]

Was there a pattern to your original reservations? I am plodding up boringly through the numbers, and would like to know whether I'm in a field from which someone else has carefully already removed the foxes ...

No real pattern. I just don't like to take 2[SUP]3[/SUP]*3*5-s right away and skip them and some other outright dead meat. Yes, of course, they all have a chance to escape, but there are chances and chances.

749640 finished very quickly (100 digits, 2^3*3*5); taking 749682
745212 now at 105 digits, 2^2*7*3^2; taking 749832

All 751k
 

Taking 751170 & 751908

For no particular reason (there are no good sequences there, honest, guv'nor!), reserving
750360
750720
750894
752880
753336
753372
753522
753870
754320
754386
754884
754992

746040 at 100 digits, 2*3^2*5
746304 at 100 digits, 2*3^2
746664 at 100 digits, 2^2 * 3 * 7
749320 at 100 digits, 2*3*5, broken in database ('Fixed index 83177760')
749682 at 100 digits, 2^2 * 3^2 * 7
749832 at 100 digits, 2^5 * 3^2

Mystery work on 740856 by someone with a slightly faster computer than mine

Taking 752528, 752760, 752928, 752970, 752976, 750040

746200 done (but database seems to be down, so I can't replace it)
Also 750040

reserving 753732

752970 at 100 digits, 2^2*3^3*7

Taking 750600

taking 750672