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Old 2020-12-04, 20:54   #24
sweety439
 
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Nov 2016
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Quote:
Originally Posted by sweety439 View Post
1. http://www.noprimeleftbehind.net/crus/
2. http://harvey563.tripod.com/
3. http://guenter.loeh.name/gc/status.html
4. http://www.fermatquotient.com/
5. https://www.rieselprime.de/Related/RieselTwinSG.htm
6. http://www.rieselprime.de/Related/LiskovetsGallot.htm
7. http://www.noprimeleftbehind.net/Car...ime-search.htm
8. http://www.noprimeleftbehind.net/gar...es-kx10n-1.htm
9. http://www.prothsearch.com/
10. https://primes.utm.edu/primes/
11. http://www.primenumbers.net/prptop/prptop.php
12. https://homes.cerias.purdue.edu/~ssw/cun/index.html
13. https://stdkmd.net/nrr/
14. https://github.com/curtisbright/mepn...ee/master/data
15. https://github.com/RaymondDevillers/primes
16. http://primegrid.com/
17. http://jeppesn.dk/generalized-fermat.html
18. http://yves.gallot.pagesperso-orange...mes/index.html
19. http://www.primefan.ru/xyyxf/default.html#0
20. https://www.rose-hulman.edu/~rickert/Compositeseq/
21. http://www.worldofnumbers.com/Append...s%20to%20n.txt
22. http://www.primenumbers.net/Henri/us/
23. https://members.loria.fr/PZimmermann...andidates.html
24. https://www.rieselprime.de/ziki/Main_Page
25. http://factordb.com/
Other pages for twin primes of the form k*2^n-1 and k*2^n+1:

http://www.noprimeleftbehind.net/gary/twins1M.htm
http://www.noprimeleftbehind.net/gary/twins100K.htm
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Old 2020-12-24, 17:13   #26
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Nov 2016
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Quote:
Originally Posted by sweety439 View Post
Other known prime factors of MMn, MWn, WMn, WWn:

MMn:

2: prime
3: prime
5: prime
7: prime
13: 338193759479, 210206826754181103207028761697008013415622289
17: 231733529, 64296354767
19: 62914441, 5746991873407, 2106734551102073202633922471, 824271579602877114508714150039, 65997004087015989956123720407169
31: 295257526626031, 87054709261955177, 242557615644693265201, 178021379228511215367151
61: unknown
89: unknown
107: unknown
127: unknown

WMn:

2: prime
3: prime
5: prime
7: prime
13: unknown (but known to be composite)
17: 2883563
19: unknown (but known to be composite)
31: unknown
61: 1328165573307087715777
89: unknown
107: unknown
127: 886407410000361345663448535540258622490179142922169401

WWn:

3: prime
5: prime
7: prime
11: 1676083, 26955961001 (cofactor is prime)
13: 67399191280564009798331, 2252735939855296339250682011
17: 349529
19: 173085275201
23: 129469791307, 36992613766212121
31: 3838477063804290331
43: unknown
61: 3290547117383710719111443
79: 183756724581423634555339057, 101874969893105185923314913883
101: unknown
127: unknown

compare with status of factors of Fermat numbers and Mersenne numbers (related links: factors of Mersenne numbers + 2 and Double Mersenne numbers)

conjecture: MMn, WMn, WWn is prime only for primes n<=7

Last fiddled with by sweety439 on 2021-06-02 at 06:20
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Old 2020-12-24, 17:20   #27
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
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Quote:
Originally Posted by sweety439 View Post
Other known prime factors of MMn, MWn, WMn, WWn:

MMn:

2: prime
3: prime
5: prime
7: prime
13: 338193759479, 210206826754181103207028761697008013415622289
17: 231733529, 64296354767
19: 62914441, 5746991873407, 2106734551102073202633922471, 824271579602877114508714150039, 65997004087015989956123720407169
31: 295257526626031, 87054709261955177, 242557615644693265201, 178021379228511215367151
61: unknown
89: unknown
107: unknown
127: unknown

WMn:

2: prime
3: prime
5: prime
7: prime
13: unknown (but known to be composite)
17: 2883563
19: unknown (but known to be composite)
31: unknown
61: 1328165573307087715777
89: unknown
107: unknown
127: 886407410000361345663448535540258622490179142922169401

WWn:

3: prime
5: prime
7: prime
11: 1676083, 26955961001 (cofactor is prime)
13: 67399191280564009798331, 2252735939855296339250682011
17: 349529
19: 173085275201
23: 129469791307, 36992613766212121
31: 3838477063804290331
43: unknown
61: 3290547117383710719111443
79: 183756724581423634555339057, 101874969893105185923314913883
101: unknown
127: unknown

compare with status of factors of Fermat numbers and Mersenne numbers

conjecture: MMn, WMn, WWn is prime only for primes n<=7
see threads:

https://mersenneforum.org/showthread.php?t=24542
https://www.mersenneforum.org/showthread.php?t=21607
https://www.mersenneforum.org/showthread.php?t=25703

Last fiddled with by sweety439 on 2020-12-24 at 17:22
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Old 2020-12-25, 00:57   #28
sweety439
 
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Factorization of Phi(n,2)
Factorization of Phi(n,10)

Smallest k>=2 such that Phi(n,k) is prime
Smallest k>=2 such that Phi(n,k,k-1) is prime

Numbers 2<=k<=4096 such that Phi(n,k) is prime
Numbers 2<=k<=4096 such that Phi(n,k,k-1) is prime

Last fiddled with by sweety439 on 2021-07-05 at 21:20
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Old 2020-12-25, 01:23   #29
sweety439
 
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Links of factorization of many types of numbers:

b^n+-1 (b<=12)
Fibonacci numbers and Lucas numbers
Fermat numbers
Generalized Fermat numbers
n!+-1
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Old 2020-12-25, 01:23   #30
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https://mers.sourceforge.io/factoredM.txt
http://mprime.s3-website.us-west-1.a...th_factors.txt
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Old 2021-01-09, 10:23   #31
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Primes of the form k*2^n+1 (Proth primes):

http://www.prothsearch.com/riesel1.html (k<=300)
http://www.prothsearch.com/riesel1a.html (301<=k<=600)
http://www.prothsearch.com/riesel1b.html (601<=k<=900)
http://www.prothsearch.com/riesel1c.html (901<=k<=1200)
https://www.rieselprime.de/ziki/Proth_prime_table (all available k values)
https://www.rieselprime.de/default.htm (many ranges of k values)
https://primes.utm.edu/top20/page.php?id=66 (top 20 page)

Primes of the form k*2^n-1 (Proth primes of the second kind):

http://www.prothsearch.com/riesel2.html (k<=300)
http://www.noprimeleftbehind.net/gar...kx2n-1-001.htm (k<=300)
http://www.noprimeleftbehind.net/gar...mes-ranges.htm
http://www.15k.org/riesellist.html (k<=300)
http://www.15k.org/Summary00300.htm (301<=k<=2000)
http://www.15k.org/Summary02000.htm (2001<=k<=4000)
http://www.15k.org/Summary04000.htm (4001<=k<=6000)
http://www.15k.org/Summary06000.htm (6001<=k<=8000)
http://www.15k.org/Summary08000.htm (8001<=k<=10000)
https://www.rieselprime.de/ziki/Riesel_prime (many ranges of k values)
https://www.rieselprime.de/default.htm (many ranges of k values)

Primes of the form k*b^k+1 (generalized Cullen primes):

http://www.prothsearch.net/cullen.html (broken link: from wayback machine cached copy) (b=2)
http://guenter.loeh.name/gc/status.html (3<=b<=100)
https://harvey563.tripod.com/GClist.txt (101<=b<=10000)
http://www.primzahlenarchiv.de/index.html (broken link: from wayback machine cached copy) (101<=b<=200)
http://www.primzahlenarchiv.de/news.html (broken link: from wayback machine cached copy) (101<=b<=200)
http://www.primzahlenarchiv.de/status.html (broken link: from wayback machine cached copy) (101<=b<=200)
https://www.rieselprime.de/ziki/Gen_Cullen_prime_table (all available bases b)
https://primes.utm.edu/top20/page.php?id=6 (top 20 page, b=2)
https://primes.utm.edu/top20/page.php?id=42 (top 20 page, b>=3)

Primes of the form k*b^k-1 (generalized Woodall primes):

http://www.prothsearch.net/woodall.html (broken link: from wayback machine cached copy) (b=2)
https://harvey563.tripod.com/GWlist.txt (3<=b<=10000)
https://harvey563.tripod.com/General...dallPrimes.txt (3<=b<=10000)
http://science.kennesaw.edu/~jdemaio/generali.htm (broken link: from wayback machine cached copy) (3<=b<=100)
https://www.rieselprime.de/ziki/Gen_Woodall_prime_table (all available bases b)
https://primes.utm.edu/top20/page.php?id=7 (top 20 page, b=2)
https://primes.utm.edu/top20/page.php?id=45 (top 20 page, b>=3)

Sophie Germain primes of the form k*2^n-1 and k*2^(n+1)-1:

https://www.rieselprime.de/Related/RieselTwinSG.htm
https://www.primepuzzles.net/problems/prob_049.htm
https://www.rieselprime.de/ziki/Cate...Sophie_Germain (k values without known Sophie Germain primes, including the k values with no possible Sophie Germain primes)
https://primes.utm.edu/top20/page.php?id=2 (top 20 page)
https://primes.utm.edu/top20/page.php?id=19 (top 20 page)

Sophie Germain primes of the second kind of the form k*2^n+1 and k*2^(n+1)+1:

https://harvey563.tripod.com/cunninghams.txt
https://www.primepuzzles.net/problems/prob_049.htm
https://primes.utm.edu/top20/page.php?id=20 (top 20 page)

Twin primes of the form k*2^n+-1:

https://www.rieselprime.de/Related/RieselTwinSG.htm
http://www.noprimeleftbehind.net/gary/twins100K.htm
http://www.noprimeleftbehind.net/gary/twins1M.htm
https://www.primepuzzles.net/problems/prob_049.htm
https://www.rieselprime.de/ziki/Cate...e_without_twin (k values without known twin primes, including the k values with no possible twin primes)
https://primes.utm.edu/top20/page.php?id=1 (top 20 page)

Index pages of these references:

http://www.prothsearch.com/
http://www.15k.org/
http://guenter.loeh.name/
https://harvey563.tripod.com/
https://www.primepuzzles.net/
http://www.noprimeleftbehind.net/gary/
https://www.rieselprime.de/Related/
https://www.rieselprime.de/default.htm
https://www.rieselprime.de/ziki/Main_Page
https://primes.utm.edu/top20/home.php

Last fiddled with by sweety439 on 2021-09-20 at 14:29
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Old 2021-01-09, 17:34   #33
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Only the top link in the last post is needed.
And rather than endlessly adding new posts, it might do well to compile these into a single pdf and attach it to the first post. Then you can update it once every week or 2 once you find more things. It will save us all from following your explorations of the internet in real time.
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