Quote:
Originally Posted by Prime95
A bold conjecture that contradicts Wagstaff's predictions. You'll need great data to back up that claim. Such as data showing that known TF factors are eliminating 3 mod 4 candidates more often than predicted.

I ran a quick count of the distinct exponents with any known factors and whether that exponent is 1 or 3 mod 4:
Mod Count
1 14,559,812 (49.301%)
3 14,972,752 (50.699%)
I wouldn't say it's a runaway for the 3 mod 4 exponents being factored. In fact it seems like a pretty basic variation around 50/50 based on an incomplete set.
If I look at the same breakdown of all exponents (below 1 billion) then it looks like (I excluded known primes, including the latest one)  spoiler alert, it's what you would expect, and probably would have come out even closer if I hadn't excluded the known primes which we know skew more (currently) to the "1" side:
Mod Count
1 25,423,460 (49.999%)
3 25,424,023 (50.001%)
EDIT: I also ran it by looking only at factors of 65bits or less, in case that matters  it does favor the "3" a little more, but not terribly. It is funny that beyond 65bits, the 1 mod 4's are ahead (by 35,474 exponents out of > 2.14 million)
Mod Count
1 13,591,041 (49.184%)
3 14,042,237 (50.816%)