Alternative Test for Primes.

[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

[rogue]

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

[mfgoode]

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

[mfgoode]

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

[Greenbank]

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.

[mfgoode]

Thank you Greenbank for this valuable information.
I presume there are still unknown primes between the ones listed.
Mally

[xilman]

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

[garo]

Come come now Paul. The showed that mally was well aware of that. Or was he?

[mfgoode]

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

[yucell]

(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?

[Greenbank]

Again, No.

2^256+1 has a factor 1238926361552897.