Please see [URL="http://www.mersennewiki.org/index.php/Sierpinski_problem_%28extended_definition%29"]http://www.mersennewiki.org/index.php/Sierpinski_problem_%28extended_definition%29[/URL] and [URL="http://www.mersennewiki.org/index.php/Riesel_problem_%28extended_definition%29"]http://www.mersennewiki.org/index.php/Riesel_problem_%28extended_definition%29[/URL] (the webpages for the lists) for more PRPs.

You proved R17!!! Also, these bases only need primility proves to be proven.

S61: (62*61^3698+1)/3 (k=43 was eliminated by you!!!)
S64: (11*64^3222+1)/3
S75: (11*75^3071+1)/2
S105: (191*105^5045+1)/8
S256: (11*256^5702+1)/3
R7: (197*7^181761-1)/2 and (367*7^15118-1)/6
R51: (1*51^4229-1)/50
R67: (25*67^2829-1)/6
R91: (1*91^4421-1)/90 and (27*91^5048-1)/2
R100: (133*100^5496-1)/33
R107: (3*107^4900-1)/2
R121: (79*121^4545-1)/6

The following PRP´s are now proven:


(215*16^3373+1)/3
(459*16^3701+1)/5
(11*75^3071+1)/2
(79*121^4545-1)/6

plus a good portion from R6, thanks to Ed for the help.



I´ve checked this thread; the following PRP´s are not-proven, yet: (not up-to date!)


(10*23^3762+1)/11
(43*93^2994+1)/4
(51*115^2736-1)/2
(3356*10^4584+1)/9
(25*67^2829-1)/6
(19*93^4362+1)/4

(11*64^3222+1)/3
(19*37^5310+1)/4
(23*27^3742-1)/2
(44*1024^1933+1)/3

(43*1024^2290-1)/3
(1*91^4421-1)/90
(169*85^6939-1)/84
(45*115^5227-1)/2
(370*8^8300+1)/7
(62*61^3698+1)/3
(10243*3^9731+1)/2
(4*115^4223-1)/3
(311*9^15668+1)/8 = (311*81^7834+1)/8

(189*31^5570+1)/10
(621*3^20820+1)/2
(191*105^5045+1)/8
(27*91^5048-1)/2
(3*107^4900-1)/2
(319*33^5043+1)/32
(133*100^5496-1)/33
(13*103^7010+1)/2.
(19*37^5310+1)/4

(79*121^4545-1)/6
(29*13^10574+1)/6

(11*256^5702+1)/3
(407*33^10961+1)/8
(29*13^10574+1)/6
(3^24761*313-1)/2
(7^15118*367-1)/6
(1*51^4229-1)/50
(2626*6^27871-1)/5
(40636*6^18749-1)/5
(152249*6^25389+1)/5
(45634*6^26606+1)/5
(144509*6^28178+1)/5
(17464*6^29081+1)/5
(93589*6^31991+1)/5
(2626*6^29061-1)/5
(2626*6^38681-1)/5
(101529*6^33532+1)/5
(170199*6^25398+1)/5
(2626*6^27871-1)/5
(54536*6^24822-1)/5
(1654*30^38869-1)/29
(197*7^181761-1)/2


Some of then where NOT loaded into factordb, I´ll do it when I start to process them. (before some-else proves them.:smile:)

[QUOTE=MisterBitcoin;484724]The following PRP´s are now proven:


(215*16^3373+1)/3
(459*16^3701+1)/5
(11*75^3071+1)/2
(79*121^4545-1)/6

plus a good portion from R6, thanks to Ed for the help.



I´ve checked this thread; the following PRP´s are not-proven, yet: (not up-to date!)


(10*23^3762+1)/11
(43*93^2994+1)/4
(51*115^2736-1)/2
(3356*10^4584+1)/9
(25*67^2829-1)/6
(19*93^4362+1)/4

(11*64^3222+1)/3
(19*37^5310+1)/4
(23*27^3742-1)/2
(44*1024^1933+1)/3

(43*1024^2290-1)/3
(1*91^4421-1)/90
(169*85^6939-1)/84
(45*115^5227-1)/2
(370*8^8300+1)/7
(62*61^3698+1)/3
(10243*3^9731+1)/2
(4*115^4223-1)/3
(311*9^15668+1)/8 = (311*81^7834+1)/8

(189*31^5570+1)/10
(621*3^20820+1)/2
(191*105^5045+1)/8
(27*91^5048-1)/2
(3*107^4900-1)/2
(319*33^5043+1)/32
(133*100^5496-1)/33
(13*103^7010+1)/2.
(19*37^5310+1)/4

(79*121^4545-1)/6
(29*13^10574+1)/6

(11*256^5702+1)/3
(407*33^10961+1)/8
(29*13^10574+1)/6
(3^24761*313-1)/2
(7^15118*367-1)/6
(1*51^4229-1)/50
(2626*6^27871-1)/5
(40636*6^18749-1)/5
(152249*6^25389+1)/5
(45634*6^26606+1)/5
(144509*6^28178+1)/5
(17464*6^29081+1)/5
(93589*6^31991+1)/5
(2626*6^29061-1)/5
(2626*6^38681-1)/5
(101529*6^33532+1)/5
(170199*6^25398+1)/5
(2626*6^27871-1)/5
(54536*6^24822-1)/5
(1654*30^38869-1)/29
(197*7^181761-1)/2


Some of then where NOT loaded into factordb, I´ll do it when I start to process them. (before some-else proves them.:smile:)[/QUOTE]

Well, can you prove (1*51^4229-1)/50 first? R51 is the smallest base only have one non-certified probable prime and only needs the primility of it to be proven, the other such bases are now R100, S105, R107 and S256. (Thanks for fully proven S61, S64, S75, R17, R67 and R121 :-)

These are the (probable) primes for k=2 and k=3 for bases 2<=b<=1024. (searched up to n=1024)

k=1 and k=4 are still reserving, I will reserve S3 after these reserves were done.

The exclusions for k<=4 are:

Sierp k=1: b=m^r with odd r>1
Sierp k=2: none
Sierp k=3: none
Sierp k=4: b=14 mod 15 and b=m^4
Riesel k=1: b=m^r with r>1
Riesel k=2: none
Riesel k=3: none
Riesel k=4: b=4 mod 5 and b=m^2

[QUOTE=sweety439;487577]These are the (probable) primes for k=2 and k=3 for bases 2<=b<=1024. (searched up to n=1024)

k=1 and k=4 are still reserving, I will reserve S3 after these reserved were done.

The exclusions for k<=4 are:

Sierp k=1: b=m^r with odd r>1
Sierp k=2: none
Sierp k=3: none
Sierp k=4: b=14 mod 15 and b=m^4
Riesel k=1: b=m^r with r>1
Riesel k=2: none
Riesel k=3: none
Riesel k=4: b=4 mod 5 and b=m^2[/QUOTE]

These are the files for k=1 and k=4.

Continue reserving S36 to n=100K

Also reserve S73, R94 (k=16), R97 (k=22), R118

Since the bases with <=3 k's remain which is not in CRUS (and not GFN or half GFN) are:

S10 k=269 (already at n=100K)
S25 k=71
S33 k=67 and 203
S36 k=1814
S42 k=13283
S60 k=4896
S67 k=17 and 21
S73 k=14
S80 k=947
S83 k=3
S93 k=67 and 87
S103 k=7
S108 k=20543
S113 k=17
S115 k=17 and 47
S117 k=59
S123 k=3 and 41
S1024 k=29, 38 and 56
R33 k=257 and 339
R42 k=1600, 6971 and 14884
R43 k=13
R60 k=16167 and 18055
R61 k=37, 53 and 100
R70 k=376, 496 and 811
R73 k=79 and 101
R85 k=61
R94 k=16
R97 k=22
R105 k=73 and 137
R108 k=5351, 6528 and 13162
R115 k=13 and 43
R118 k=43
R123 k=11
R1024 k=31, 56 and 61

However, srsieve and sr2sieve cannot run both b and k are odd, thus some odd bases cannot be run by them, and I reserve S36, S73, R94, R97 and R118 first, then do S42, S60, S80, S108, S1024, R42, R60, R70, R108 and R1024.

[QUOTE=sweety439;487616]Continue reserving S36 to n=100K

Also reserve S73, R94 (k=16), R97 (k=22), R118

Since the bases with <=3 k's remain which is not in CRUS (and not GFN or half GFN) are:

S10 k=269 (already at n=100K)
S25 k=71
S33 k=67 and 203
S36 k=1814
S42 k=13283
S60 k=4896
S67 k=17 and 21
S73 k=14
S80 k=947
S83 k=3
S93 k=67 and 87
S103 k=7
S108 k=20543
S113 k=17
S115 k=17 and 47
S117 k=59
S123 k=3 and 41
S1024 k=29, 38 and 56
R33 k=257 and 339
R42 k=1600, 6971 and 14884
R43 k=13
R60 k=16167 and 18055
R61 k=37, 53 and 100
R70 k=376, 496 and 811
R73 k=79 and 101
R85 k=61
R94 k=16
R97 k=22
R105 k=73 and 137
R108 k=5351, 6528 and 13162
R115 k=13 and 43
R118 k=43
R123 k=11
R1024 k=31, 56 and 61

However, srsieve and sr2sieve cannot run both b and k are odd, thus some odd bases cannot be run by them, and I reserve S36, S73, R94, R97 and R118 first, then do S42, S60, S80, S108, S1024, R42, R60, R70, R108 and R1024.[/QUOTE]

S10 is already at n=100K, and the bases above such that srsieve and sr2sieve cannot run are S25, S33, S67, S83, S93, S103, S113, S115, S117, S123, R33, R43, R61 (except k=100), R73, R85, R105, R115 and R123.

[QUOTE=sweety439;487616]Continue reserving S36 to n=100K

Also reserve S73, R94 (k=16), R97 (k=22), R118

Since the bases with <=3 k's remain which is not in CRUS (and not GFN or half GFN) are:

S10 k=269 (already at n=100K)
S25 k=71
S33 k=67 and 203
S36 k=1814
S42 k=13283
S60 k=4896
S67 k=17 and 21
S73 k=14
S80 k=947
S83 k=3
S93 k=67 and 87
S103 k=7
S108 k=20543
S113 k=17
S115 k=17 and 47
S117 k=59
S123 k=3 and 41
S1024 k=29, 38 and 56
R33 k=257 and 339
R42 k=1600, 6971 and 14884
R43 k=13
R60 k=16167 and 18055
R61 k=37, 53 and 100
R70 k=376, 496 and 811
R73 k=79 and 101
R85 k=61
R94 k=16
R97 k=22
R105 k=73 and 137
R108 k=5351, 6528 and 13162
R115 k=13 and 43
R118 k=43
R123 k=11
R1024 k=31, 56 and 61

However, srsieve and sr2sieve cannot run both b and k are odd, thus some odd bases cannot be run by them, and I reserve S36, S73, R94, R97 and R118 first, then do S42, S60, S80, S108, S1024, R42, R60, R70, R108 and R1024.[/QUOTE]

S73 at n=15387
R94 at n=14115
R97 at n=15005
R118 at n=15629

All no (probable) prime found.

Reserve S22 for the k's not in CRUS (i.e. gcd(k+1,22-1) is not 1).

Update the sieve file.

Reserve R22 for the k's not in CRUS (i.e. gcd(k-1,22-1) is not 1).

Update the sieve file.

Reserve S28 for the k's not in CRUS (i.e. gcd(k+1,28-1) is not 1).

Update the sieve file.