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Old 2003-09-27, 10:10   #1
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Sep 2003

50248 Posts
Default Exponents that haven't had a P-1 test done

First column is Meg range (for instance, 6 = 6,000,000 - 6,999,999).

Second column is the number of exponents in that range for which 2 matching LL tests were done with no P-1 factoring ever having been done for that exponent.

 0      0
 1      0
 2  15152
 3  24580
 4  18831
 5   9243
 6   4170
 7   1916
 8   1454
 9   2754
10    140
11     23
12      8
13      6
14      2
15      8
16      3
17      2
18      3
19      1
How do we interpret these results?

At low ranges (2M - 4M), there's a lot. That's because P-1 wasn't added to Prime95 until fairly recent versions, so old exponents got two LL double-checks done and that was all.

At very low ranges (0M - 1M) however, the number drops to zero, because someone is systematically P-1 trial-factoring all those old small exponents and they've gotten up to about 2.4M.

At higher ranges (5M - 8M) the numbers drop steadily because P-1 factoring got added to Prime95 and the chances are reasonable that at least one of the two computers involved had enough memory to do a P-1 test. Still, thousands of exponents never got a P-1 test done.

Finally at the highest ranges (10M +) the numbers are low because most exponents simply haven't been double-checked yet. The leading edge of double-checking is currently sweeping past 10.2M. If every single exponent got a P-1 test before a second LL test was performed, those numbers would stay permanently low and a few dozen new factors would be found in each Meg range, assuming a 3% or so chance of finding a P-1 factor.

I'm not sure why the count picks up sharply in the 9M range after steadily declining. Any ideas?

Last fiddled with by GP2 on 2003-09-27 at 10:11
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