I'm curious as to the history of how the exponent was/is chosen for the various SGS (and twin prime search) ranges that we've searched over the years. I believe that TPS (before my time) searched n=333333, and SGS mostly did n=666666 and now n=1.29M. I believe the immediate answer is that there had been heavy sieving done, making LLR efficient to run on those ranges. But that of course just begs the question as to why those ranges had been heavily sieved. Is there something "special" about those n's (other than the repeated digits, of course), or would it be equally valid/productive to search n=314159 or n=987987 or n=1234567? Assuming the sieving were done for those n, of course.

I did find a board post from Lennart saying (in part) that n=1.29M keeps us under a particular FFT size threshold.

Just curious.

--Gary
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"I am he as you are he as you are me and we are all together"

87*2^3496188+1 is prime! (1052460 digits)
4 is not prime! (1 digit)

One reason is that you mentioned, particular FFT size threshold.

The other reason is that we want to keep SGS in Top5000 as long as possible, which needs to be considered together with PPSe progress.
New SGS primes are entering ~1700 place and pushing all PPSe primes down (entering 3000 - 3500). Once PPSe crosses 1290k (with leading edge being around 1248k), it will start pushing all SGS down.

btw, TPS was done also for n=195000.
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