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Old 2006-02-14, 12:54   #1
mfgoode
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Lightbulb Alternative Test for Primes.

Alternative Test for Primes.
I quote from TAOCOP by Donald E. Knuth.
“The worlds largest explicitly known primes have always been Mersenne primes.
But the situation might change since M/Primes are getting harder to find”

Testing numbers of the form N =5.2^n + 1` for primality with the same number of squarings mod N as the LL test should be a feasible alternative.
Mally
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Old 2006-02-14, 13:08   #2
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Quote:
Originally Posted by mfgoode
Alternative Test for Primes.
I quote from TAOCOP by Donald E. Knuth.
“The worlds largest explicitly known primes have always been Mersenne primes.
But the situation might change since M/Primes are getting harder to find”

Testing numbers of the form N =5.2^n + 1` for primality with the same number of squarings mod N as the LL test should be a feasible alternative.
Mally
Already being tested at http://www.prothsearch.net
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Old 2006-02-14, 13:16   #3
mfgoode
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Question Alternative Test for Primes

Quote:
Originally Posted by rogue
Already being tested at http://www.prothsearch.net
Correct me if Im wrong but the numbers I have given are are +1 not -1. I confess Im not much into this type.
Mally
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Old 2006-02-14, 15:27   #4
mfgoode
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Cool Alternate Test for Primes

Quote:
Originally Posted by mfgoode
Correct me if Im wrong but the numbers I have given are are +1 not -1. I confess Im not much into this type.
Mally
:surprised Sorry I took a cursory check on the URL before I posted. A second check gave me the answer. Well I learnt something on Proth Primes.
Mally
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Old 2006-02-16, 17:00   #5
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If you look at: http://primes.utm.edu/largest.html you'll notice the top 5 primes are Mersenne (M43? to M39?), and 4 of the remaining 5 are Proth primes. The 8th largest known prime is M38.
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Old 2006-02-16, 18:02   #6
mfgoode
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Exclamation Alternate Test for Primes

Thank you Greenbank for this valuable information.
I presume there are still unknown primes between the ones listed.
Mally
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Old 2006-02-16, 20:09   #7
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Quote:
Originally Posted by mfgoode
Thank you Greenbank for this valuable information.
I presume there are still unknown primes between the ones listed.
Mally
Don't be silly.

The number of primes less than N is about N/logN. Where are you going to fit all the primes smaller than the largest known prime? The number of such primes is itself vastly greater than the second-largest known prime.


Paul
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Old 2006-02-16, 23:27   #8
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Come come now Paul. The showed that mally was well aware of that. Or was he?
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Old 2006-02-19, 16:25   #9
mfgoode
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Thumbs down Alternative Test for Primes

Quote:
Originally Posted by garo
Come come now Paul. The showed that mally was well aware of that. Or was he?
Thank you Garo. Of late, Paul is indulging in reading a different meaning
in straight forward posts . He enters into a labyrinth of ideas and knots himself up. You know Festus' assessment of Paul (The apostle)"much-- learning has......"
Mally
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Old 2006-02-28, 09:30   #10
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(2^k)+1=prime????

k for 2=5

k for 4=17

k for 16=65537

k for 256=............

k for 65536=.............

k for 4294967296=...............

can it be?
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Old 2006-02-28, 11:53   #11
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Again, No.

2^256+1 has a factor 1238926361552897.
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