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Message boards :
Sophie Germain Prime Search :
SGS primes and the Top 5000 List
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John Honorary cruncher
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The day is quickly approaching when SGS single primes will no longer make it into the Top 5000 List. We are about 4 weeks away from the 5000th prime being larger than 200700 digits which is the size of SGS primes.
We are ~62% through the search space with no success. We are on the unlucky side now to not have found a twin or a Sophie Germain. Even with single primes falling off the Top 5000 list, we'll continue to search for at least one of these significant primes. A find for either will be a World Record. :)
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HonzaVolunteer moderator
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Good estimation - those of 2^666666-1 are entering 4950 right now...getting tight.
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My main page is showing a hit on SGS. It would be my first prime (not counting PRPNet). No info is available, though:
http://www.primegrid.com/primes/?section=primelist&userid=59072
How long will it take to be reported?
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676754^262144+1 is prime | |
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HonzaVolunteer moderator
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It took no so long, already there: 6515132744445*2^666668-1 - congrats on prime.
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JohnHonorary cruncher
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The day is quickly approaching when SGS single primes will no longer make it into the Top 5000 List. We are about 4 weeks away from the 5000th prime being larger than 200700 digits which is the size of SGS primes.
Although 2 weeks longer than the original estimate, the end is soon approaching. Trailing edge primes are failing to make the Top 5000 while leading edge primes are entering ~4985. Primes are being submitted as they are validated, even before SG/twin testing is completed. Don't worry, it's easy to retro an SG/twin prime should one present itself.
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I read somewhere in the forum (can't remember where) that as soon as a certain range of k was completed or a SG prime was found, we would begin sieving and afterwards searching a higher range of n (so that they'd be large enough to make the top 5000 list again).
I was just wondering what the progress of that was... | |
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It was "only" found a twin, not a Sophie. Search for Sophie is ongoing at the same ranges like before.
Regards Odi
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...that didn't really answer my question.
I was asking about the future of the SGS search, if and when we switch to another range... | |
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Once a SG prime is found, PrimeGrid will begin a new range, with higher n values. | |
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JohnHonorary cruncher
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....I was asking about the future of the SGS search, if and when we switch to another range...
The plan was to finish off the current SGS search at n=666666 with hopes that an SG prime would be found. Then the goal was to collaborate with David Underbakke again in two specialized sieves for SGS and TPS. Both sieves would again have the possibility of finding each other's form as well as the addition of a Cunningham Chain form. Yes, this would rejuvenate the TPS project...and open up the badge again. :)
Depending on whether or not an SG prime is found at n=666666, the next SG search would either increase in n or decrease. The current SG record is 183027*2^265440-1. As you can see, n is substantially lower than our current range of n=666666.
The TPS search would be at n=1010101. With twins at 333333 and 666669, the next logical step would be 999999. However, because of PG's success, the expectation now is for a megabit twin. n=1010101 is a good choice since it has nice symmetry and it would be a fitting symbolic gesture to binary code.
If you take this natural progression you'll figure out that, when the software/hardware are of proper caliber, the goal will eventually lead to the search for twin mega primes. But that's still quite a ways down the road.
Unfortunately, the ideas were tabled.
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Unfortunately, the ideas were tabled.
So, and pardon my slowness, where does that leave SG and it's future? | |
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HonzaVolunteer moderator
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Yes, this would rejuvenate the TPS project...and open up the badge again. :)
Oh, yeah! Come on...
BONIC is at 31.5T, PRPNet is down to 38.5T, so there are ~7T left? With ~450k test per 1T, still would leave ~3M tests. Is that correct?
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JohnHonorary cruncher
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Unfortunately, the ideas were tabled.
So, and pardon my slowness, where does that leave SG and it's future?
In limbo...however, there's probably 6 months remaining of SGS work at n=666666 so plenty of time to discuss future plans.
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Message boards :
Sophie Germain Prime Search :
SGS primes and the Top 5000 List |
