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Message boards : General discussion : fully prime searched range?

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[SG]Puzzle-Peter
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Message 10662 - Posted: 12 Sep 2008 | 17:30:20 UTC

Couldn't find the answer to this question:

all those prime search projects are looking for big prime numbers of certain specific characteristica, Proth, Sierpinski etc. That means we are probably missing a lot of primes between the ones we find. Up to which number do we know ALL primes? Is there anybody trying to extend that range?

Thanks, Peter

AlphaLaser

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Message 10663 - Posted: 12 Sep 2008 | 17:58:28 UTC

PrimeGrid once ran the primegen project which actually did a comprehensive sequential search of all numbers from 3 on up. You can torrent the final results here. The page indicates that the upper bound for the numbers is 210 000 000 000. However, thats minuscule compared to the numbers searched by Cullen-Woodall/TPS/etc., because primes of certain specific forms can be checked much more efficiently.

The primegen project was retired though and I am unaware of anyone else who is continuing to do a sequential search and/or searched a larger space than PrimeGrid.
____________

Marcus

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Message 10664 - Posted: 12 Sep 2008 | 18:07:32 UTC

There's no point doing a comprehensive search, because we don't have the storage capacity for all those primes. At least until Google makes a free online service with infinite gigabytes, then we'll continue.
Anything we can guess about the distribution of primes, we can guess from the ones already known. If someone wants a certain sized prime, there are free programs for that. Primes of special forms are more interesting, because we can search for them faster, and they might be good for something sometime (a good excuse for anything in mathematics).

[SG]Puzzle-Peter
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Message 10666 - Posted: 13 Sep 2008 | 5:48:55 UTC