Update this file to show that there are no k remain for S2 with 271129 (2nd CK for S2) < k < 271577 (3rd CK for S2).

See [URL="http://www.mersennewiki.org/index.php/1st%2C_2nd_and_3rd_Sierpinski_conjectures"]http://www.mersennewiki.org/index.php/1st%2C_2nd_and_3rd_Sierpinski_conjectures[/URL] (Sierpinski) and [URL="http://www.mersennewiki.org/index.php/1st%2C_2nd_and_3rd_Riesel_conjectures"]http://www.mersennewiki.org/index.php/1st%2C_2nd_and_3rd_Riesel_conjectures[/URL] (Riesel) for these conjectures.

R9 k=386 and 744 tested to n=25K, no primes found, base released.

Update the result file.

R12 currently at n=21760, no other primes found.

[QUOTE=sweety439;490302]R12 currently at n=21760, no other primes found.[/QUOTE]

Only these primes found: (except k=846)

1057*12^690+1
1057*12^1072+1
1057*12^1522+1
563*12^4020+1
1052*12^5715+1
1057*12^6514+1
1057*12^6826+1
1057*12^7438+1

No prime found for k = 885, 911, 976, 1041 for n<=25K.

Update the result file.

S3 currently at n=16354.

A (probable) prime found:

(3061*3^15772+1)/2

I´ve checked this thread; the following PRP´s are not-proven, yet:

Reserved PRP´s

(459*16^3701+1)/5

Unreserved PRP´s; please not that some of them are unprovable!


(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
(22^3634*464+1)/3
(22^3720*1161+1)/7

(19*93^4362+1)/4
(22^4121*1793+1)/3

(11*64^3222+1)/3
(19*37^5310+1)/4
(23*27^3742-1)/2
(44*1024^1933+1)/3
(22^5596*953+1)/3
(22^5794*464+1)/3
(22^2626*697-1)/3
(22^2787*1588-1)/3
(22^2955*2623-1)/3
(22^3073*355-1)/3
(22^3236*2230-1)/3
(22^3390*997-1)/3
(22^3790*697-1)/3
(22^4035*1588-1)/3
(22^4270*2276-1)/7
(28^2938*1507-1)/3
(28^3954*472-1)/3
(28^4324*2464-1)/3
(28^4956*1159-1)/3
(28^5400*460-1)/27

(28^5718*472-1)/3
(22^5339*883-1)/21
(22^6617*2116-1)/3
(22^6987*2623-1)/3
(22^7447*883-1)/21
(22^8046*2083-1)/3
(43*1024^2290-1)/3
(22^10330*1814+1)/3
(22^6408*355-1)/3
(22^6543*355-1)/3

(22^7020*1343+1)/21
(22^8386*953+1)/3
(1*91^4421-1)/90
(28^8536*1159-1)/3
(28^9147*3232-1)/9
(22^8616*763-1)/3
(22^9543*1588-1)/3
(22^12106*883-1)/21
(22^12211*2623-1)/3

(28^7059*472-1)/3
(28^7073*3019-1)/3
(28^8121*460-1)/27
(22^3371*2116-1)/3
(28^9210*460-1)/27
(169*85^6939-1)/84
(22^9671*2719-1)/3
(22^12674*2536-1)/3
(22^9891*2623-1)/3
(2719*22^9671-1)/3
(45*115^5227-1)/2
(370*8^8300+1)/7
(22^3897*1161+1)/7
(3061*3^15772+1)/2
(28^14418*1364+1)/3
(28^10390*1507-1)/3
(62*61^3698+1)/3
(10243*3^9731+1)/2
(28^10718*460-1)/27
(28^11474*472-1)/3
(22^16620*461+1)/21
(28^14418*1364+1)/3
(28^13548*460-1)/27
(22^12661*953+1)/3
(22^16219*1814+1)/3
(4*115^4223-1)/3
(28^5459*1043+1)/9
(28^2938*1507-1)/3
(311*9^15668+1)/8 = (311*81^7834+1)/8
(189*31^5570+1)/10
(28^3954*472-1)/3
(621*3^20820+1)/2
(191*105^5045+1)/8
(27*91^5048-1)/2
(3*107^4900-1)/2
(28^8607*1565+1)/27
(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
(28^20170*1507-1)/3
(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
(14*73^21369+1)/3
(2626*6^38681-1)/5
(101529*6^33532+1)/5
(170199*6^25398+1)/5
(2626*6^27871-1)/5
(16*94^21951-1)/3
(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:)

Extended Sierpinski problems:

[URL="https://docs.google.com/document/d/e/2PACX-1vRH8VX4Zo9Lu4pIBuM7opEo_GkTC3oNE9-UvSeg2QzEDWowTrsQEl1yF0A-Kc8EygVlkbbwhA61qNP2/pub"]https://docs.google.com/document/d/e/2PACX-1vRH8VX4Zo9Lu4pIBuM7opEo_GkTC3oNE9-UvSeg2QzEDWowTrsQEl1yF0A-Kc8EygVlkbbwhA61qNP2/pub[/URL]

Extended Riesel problems:

[URL="https://docs.google.com/document/d/e/2PACX-1vSh5ny4s0c3Hu6R__ao1XHPSo6QAMG8RLPShcepS9AdIRNAyDu-GAYHw7oY9Fi0gSaOXljfqGrS5AcH/pub"]https://docs.google.com/document/d/e/2PACX-1vSh5ny4s0c3Hu6R__ao1XHPSo6QAMG8RLPShcepS9AdIRNAyDu-GAYHw7oY9Fi0gSaOXljfqGrS5AcH/pub[/URL]

Note: gcd(m,0) = m for all integer m, and gcd(m,1) = 1 for all integer m.

Besides, for R35, k=1, the formula is (1*35^n-1)/gcd(1-1,35-1) = (1*35^n-1)/gcd(0,34) = (1*35^n-1)/34, and we allow n=1 (but we do not allow n=0, all n must be >=1), however, (1*35^1-1)/34 = 34/34 = 1 is not considered prime, and the smallest prime of this form is (1*35^313-1)/34, the corresponding n is 313.

Since we allow n=1 but not allow n=0, thus for example S2, the corresponding prime for k=7 and k=14 are both 29 ((7*2^2+1)/gcd(7+1,2-1) and (14*2^1+1)/gcd(14+1,2-1)), but the corresponding for k=28 is 113 ((28*2^2+1)/gcd(28+1,2-1), not 29 = (28*2^0+1)/gcd(28+1,2-1), the same prime (29) for k=7 n=2 and k=14 n=1 would be k=28 n=0, but n must be n>=1 hence it is not allowed).

Record of n's and the corresponding k's (include the k's > CK, if this conjecture is proven): (k's make a full covering set with all or partial algebraic factors should not be included)

S2: (conjectured k's: {78557, 157114, 271129, 271577, ...})

[CODE]
k n
1 1
4 2
12 3
16 4
19 6
31 8
47 583
383 6393
2897 9715
3061 33288
4847 3321063
5359 5054502
10223 31172165
21181 >31600000
[/CODE]

S3: (conjectured k's: {11047, ...})

[CODE]
k n
1 1
5 2
16 3
17 6
21 8
41 4892
621 20820
1187? >10000
[/CODE]

S4: (conjectured k's: {419, 659, 794, ...})

[CODE]
k n
1 1
6 2
19 3
30 4
51 46
86 108
89 167
94 291
186 10458
1238? ?
[/CODE]