Here's a question that someone (not me!) will solve easily (I'm a
distributed computing fan, not a math person).

I just found 4 factors in a row from exponents randomly assigned by the
project.  They were found by my venerable Dell 300 MHz running Prime 95
v 22.12.1.  They are:

[Fri Feb 14 21:07:28 2003]
UID: DHPope/Dell_D300, M21854477 has a factor: 45928782121719444089
[Fri Feb 14 23:41:02 2003]
UID: DHPope/Dell_D300, M22097233 has a factor: 3217100536856962057
[Fri Feb 28 13:14:53 2003]
UID: DHPope/Dell_D300, M22234129 has a factor: 140822725249178815159
UID: DHPope/Dell_D300, M22234361 has a factor: 175724459936280049

The series stops at 4, because since then I've run a fifth exponent
whose factor was not found.

What's interesting to me is that the factor of the second exponent was
found only about 2.5 hours after the finding of the first, and the
fourth was found immediately as it started running.

So, what's the chance of finding factors using Prime 95's default
settings for four randomly assigned exponents in a row?

Hey!  This could be a footnote somewhere, don't you think?!?

Best regards,
Dennis Pope
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