20190605, 08:11  #45 
Mar 2006
Germany
3^{2}×5^{2}×13 Posts 
I've included a separate page for all remaining data for Williams primes (for now only MMtype).
Listed are all bases b < 2050 not yet available as own page and nmax=1000 or given range. 
20190609, 00:02  #46 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
5·13·47 Posts 
In the page Proth prime small bases least n, the data is not correct: the forms 2*512^n+1, 4*32^n+1, 4*512^n+1, 4*1024^n+1, 10*1000^n+1 and 12*12^n+1 may have primes, since it is not known whether there are Fermat primes > 2^(2^4)+1, etc. (all these numbers are generalized Fermat numbers). (Note that such forms do not include 8*128^n+1, 8*128^n+1 have no possible primes)
Also, recently a prime 7*1004^54848+1 was found, please add it. 
20190610, 20:07  #47 
"Dylan"
Mar 2017
2·293 Posts 

20190614, 09:14  #48 
Mar 2006
Germany
2925_{10} Posts 

20190615, 04:44  #49  
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
5×13×47 Posts 
Quote:
* Base 512: Proth prime 511•2^{n}+1 (first nvalue divisible by 9) * Base 817: Conjectures 'R Us not started yet Like the notes in Williams MM: * Base 128: Riesel prime 127•2^{n}1 (first nvalue divisible by 7) * Base 478: Conjectures 'R Us not started yet 

20190615, 04:58  #50 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
3055_{10} Posts 
The note for the data list in the page Proth prime small bases least n is not correct, some forms are also generalized Fermat numbers but with known primes (such as 2*8^n+1, 4*2^n+1, 6*6^n+1, etc.), and there are numbers instead of "" in the list for these forms, however, for generalized Fermat numbers without known primes (such as 2*512^n+1, 4*32^n+1, 12*12^n+1, etc.), there are "" in the list, these forms have no known primes, like all current 0's in the list (such as 2*365^n+1, 4*53^n+1, 5*308^n+1, etc.), all of these forms have no known primes. Do you think the generalized Fermat numbers (2*512^n+1, 4*32^n+1, 12*12^n+1, ...) should be listed in the "Wanted values" section? They also have the Nash Weight, and there are no known primes of the form 2*512^n+1, like there are also no known primes of the form 2*365^n+1.
(I know that CRUS excludes the generalized Fermat numbers like 2*512^n+1 from searching, but some problems requires the generalized Fermat numbers, e.g. the "minimal primes problem", finding all minimal primes in given base, for base 32, the form 4{0}1 (4000...0001) is generalized Fermat numbers 4*32^n+1, and for my problem A Sierpinski/Riesellike problem, I do not exclude generalized Fermat numbers like 4*32^n+1 from searching and consider the problem S32 is not proven and with k=4 remain. Last fiddled with by sweety439 on 20190615 at 05:04 
20190617, 17:18  #51 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
5757_{8} Posts 
Category: Reserved contains Williams MP reserved by CRUS (123, 342, 438, 487, 757, 997, 1005) but does not contain Williams PP reserved by CRUS (327 and 1017).
Last fiddled with by sweety439 on 20190617 at 17:18 
20190618, 13:03  #52 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
5×13×47 Posts 
Currently Category:Reserved does not contain Williams MM 268, which is also reserved by CRUS.

20190618, 13:06  #53 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
5757_{8} Posts 
Williams PM 25 has a remark that this should be (re)used from base 5, but Williams MM 25 and Williams MP 25 do not have, is this true for all perfect power bases (4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81, 100, 121, 125, 128, 144, 169, 196, 216, 225, 243, 256, 289, 324, 343, 361, 400, 441, 484, 512, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1000, 1024, ...) for all four kinds of Williams primes and for Carol/Kynea primes? (I know that this is not true for generalized Cullen/Woodall primes)

20190618, 19:33  #54 
Mar 2006
Germany
101101101101_{2} Posts 
This remark is still only a reminder, so not used on other bases than powers of 2. Therefore I will not update all perfect power bases for now.
Checking the source of such pages using another base you will find the automatic generation of the nvalues. To avoid double work all sequences should be listed as their normalized form so instead of searching 3*4^n1 search 3*2^n1 and generate the first sequence from that. So if a new 3*2^n1prime is found, only this sequence has to be edited, the other seq. will updated on the fly:  less editing  less type errors For now I've used this only for Carol/Kynea or Williams like primes, the latter are using Riesel or Prothtype lists (base 2 only). If I will include other bases this could be extended to forms like Williams PM 25. I've extended the Williams template to show a grey base if it uses a normalized power of 2 base sequence like as used for Carol/Kynea. 
20190623, 10:45  #55 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
5757_{8} Posts 
If a prime in the list is also other classes of primes, I think it should be in the notes, like the article Riesel 3, the prime 3*2^61 is also Sophie Germain (since 3*2^71 is also prime), twin (since 3*2^6+1 is also prime), and NearWoodall (since 3*2^61 = (5+1)*2^51), however, for the article Williams MP 5, ALL such primes are also generalized Fermat (since all are also of the form x^2+1, since all such n's are even, and thus 4*5^n is a square), but current only 20462 and 70130 has this note.
Sophie Germain: prime k*2^n1 such that k*2^(n+1)1 is also prime Sophie Germain of the second kind: prime k*2^n+1 such that k*2^(n+1)+1 is also prime Cunningham chains with length r: k*2^n1, k*2^(n+1)1, ..., k*2^(n+r1)1 are all primes Cunningham chains of the second kind with length r: k*2^n+1, k*2^(n+1)+1, ..., k*2^(n+r1)+1 are all primes Sophie Germain with order b: prime k*b^n1 such that k*b^(n+1)1 is also prime Sophie Germain of the second kind with order b: prime k*b^n+1 such that k*b^(n+1)+1 is also prime Cunningham chains with length r and order b: k*b^n1, k*b^(n+1)1, ..., k*b^(n+r1)1 are all primes Cunningham chains of the second kind with length r and order b: k*b^n+1, k*b^(n+1)+1, ..., k*b^(n+r1)+1 are all primes Twin: k*b^n1 and k*b^n+1 are both primes Cullen base b: n*b^n+1 Woodall base b: n*b^n1 Carol base b: (b^n1)^22 Kynea base b: (b^n+1)^22 Williams MM base b: (b1)*b^n1 Williams MP base b: (b1)*b^n+1 Williams PM base b: (b+1)*b^n1 Williams PP base b: (b+1)*b^n+1 NearCullen/Woodall MM base b: (n1)*b^n1 NearCullen/Woodall MP base b: (n1)*b^n+1 NearCullen/Woodall PM base b: (n+1)*b^n1 NearCullen/Woodall PP base b: (n+1)*b^n+1 Fermat base b: b^(2^n)+1 Repunit base b: (b^n1)/(b1) Wagstaff base b: (b^n+1)/(b+1) 
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