20110726, 23:54  #1 
Jun 2011
Henlopen Acres, Delaware
7·19 Posts 
Continuity of Primes
With all of the various ways to generate primes (Riesel, Proth, Mersenne etc) there seems to be quite a few "gaps" that must occur in the "plain old" primes that can't be expressed with an elegant, concise formula that lends itself to fast primality proving.
Is there any such list of "known continuous primes" where all the primes < P have been identified? That would be the real "No Primes Left Behind" effort I would think. 
20110727, 01:53  #2 
Jun 2003
7×167 Posts 

20110727, 07:17  #3 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT)
2^{2}·5·283 Posts 
Primegrid had a subproject that found contiuous primes. They ended up with with many dvds of data.

20110727, 11:12  #4 
Einyen
Dec 2003
Denmark
2,833 Posts 
Here you can find the first 10^{12} primes up to 3*10^{13}:
http://primes.utm.edu/nthprime/ 
20110729, 23:19  #5  
Jun 2011
Henlopen Acres, Delaware
205_{8} Posts 
Quote:
If that is true, each prime is probably a unique find. Correct? 

20110730, 15:07  #6  
Jun 2003
7×167 Posts 
Quote:
If you expended 100 times as much effort, you might get up to 10^21. If you devoted the entire world's computer resources to the project, you could probably push it well past 10^30. You'd never, ever, reach this 100 digit prime: 3664461208681099176204078925954510073897620111029087350504719136242910190767917650858670935504633223 Quote:
3664461208681099176204078925954510073897620111029087350504719136242910190767917650858670935504633509 Both took a fraction of a second to generate on my computer. Neither, in all probability, has ever been "discovered" before. The primes that are considered "discoveries" are the ones that take significant resources to find I suggest you read this primer on primality testing. You'll have a much better understanding of what you see in this forum. 

20110803, 03:20  #7  
Jun 2011
Henlopen Acres, Delaware
133_{10} Posts 
Quote:
The first answer you gave answers this one. With such a huge gap in the prime record, there is no way any of the primes we generate here are a part of that continuous list. I thought maybe there were people somewhere who would test the neighborhood of announced primes for primality as well, perhaps "finding" some that might have been shown later. Now I see that was a stupid assumption! So each prime that is found is, essentially, a new find. I'd call that a discovery. The large primes you mentioned I would call a "monumental undertaking" as well. Quote:


20110803, 04:38  #8  
Jun 2011
Henlopen Acres, Delaware
7·19 Posts 
Quote:
In 2002 a long standing question was answered: can integers be prove prime I think this should be changed to the word proven there. And now I actually know how to do the LucasLehmer test, although those s(k) numbers grow too big for Excel after s(4). At least Excel can prove 2^5  1 is prime using LucasLehmer Last fiddled with by LiquidNitrogen on 20110803 at 04:38 

20110803, 14:49  #9 
Aug 2006
2^{2}·5·293 Posts 
If you reduce mod the Mersenne number at each step, you can prove 2^19  1 prime in Excel.

20110803, 15:11  #10  
Jun 2011
Henlopen Acres, Delaware
133_{10} Posts 
Quote:
1. Proving p = 2^n  1 is prime for n = 5, p = 31. 2. S(0) = 4 {defined} 3. Need to generate up to S(n2) where S(x+1) = [S(x) * S(x)]  2 3a. S(1) = 4^2  2 = 14 3b. S(2) = 14^2  2 = 194 3c. S(3) = 194^2  2 = 37634 4. Test S(n2)/p = S(3)/p = 37634/31. If remainder is 0, p is prime. 37634/31 = 1214.0 so p is prime. What would this involve doing it the way you mentioned? Last fiddled with by LiquidNitrogen on 20110803 at 15:18 

20110803, 15:24  #11  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
5,431 Posts 
Quote:


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