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Message boards : General discussion : Numbers like GFN

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Crun-chi
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Message 68953 - Posted: 5 Sep 2013 | 23:09:46 UTC

As I can see, those numbers have N= 65536, 131072, 262144....

Three questions:

1. Can I made sieve and search primes for example N=111111 (k*111111+1)
2. How to make that sieve?
3. Is it will be any primes in such condition :) ?

I know in that case it wont be GF numbers, but will be something that never be searched :)
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92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
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Iain Bethune
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Message 68959 - Posted: 6 Sep 2013 | 9:57:19 UTC - in response to Message 68953.

Hi Crun-chi,

No idea on the sieving (although one could do a simple trial division filter). But in general, testing such numbers for primes will be really slow, so you will be stuck with small numbers i.e. below top5000 list. Fast tests only exist for a range of particular forms e.g. Proth, Riesel, Mersenne, GFN, Primorial etc.

Probably best thing to look at is: http://mersennewiki.org/index.php/Primality_test or check out LLR and PFGW as they implement almost all of the fast deterministics tests and PRP checks.

Otherwise you'll be using ECPP - for reference the record ECPP-proved prime has a little over 26,000 digits! http://primes.utm.edu/top20/page.php?id=27

As always, happy hunting!

- Iain
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3073428256125*2^1290000-1 is Prime!

Crun-chi
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Message 68961 - Posted: 6 Sep 2013 | 11:31:49 UTC - in response to Message 68959.

Thanks for answer my question :)
Since only speed can provide to me number of candidates& better probability I am forced to stick with "ordinary" sieving and prime proving methods, and my idea dont stick with no one above :)

____________
92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
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Ken_g6
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Message 69051 - Posted: 10 Sep 2013 | 0:09:31 UTC

If you meant to say k^111111+1, looks like the answer is no. In your case, apparently, k^37037+1 | k^111111+1 (for all k!)

It apparently doesn't work for -1 either.
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Crun-chi
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Message 69089 - Posted: 11 Sep 2013 | 12:18:26 UTC - in response to Message 69051.

So my idea is useless :)
____________
92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie!

Message boards : General discussion : Numbers like GFN