[QUOTE=sweety439;487923]S73 is proven!!! One (probable) prime was found:

(14*73^21369+1)/3

Base released (currently at n=24007).

R94 has also one (probable) prime found:

(16*94^21951-1)/3 (currently at n=22303)

Now only k=29 needs a prime, and this k has already been searched to n=1M by CRUS, this base also released.

R97 tested to n=23113, no (probable) prime found.

R118 tested to n=24257, no (probable) prime found.[/QUOTE]

R97 at n=35817, R118 at n=37013, both no (probable) prime found.

Now these (probable) primes are found:

S22:

(1343*22^1878+1)/gcd(1343+1,22-1)
(464*22^2082+1)/gcd(464+1,22-1)
(1814*22^2859+1)/gcd(1814+1,22-1)
(464*22^3634+1)/gcd(464+1,22-1)
(1161*22^3720+1)/gcd(1161+1,22-1)
(1161*22^3897+1)/gcd(1161+1,22-1)
(1793*22^4121+1)/gcd(1793+1,22-1)
(953*22^5596+1)/gcd(953+1,22-1)
(464*22^5794+1)/gcd(464+1,22-1)
(1343*22^7020+1)/gcd(1343+1,22-1)
(953*22^8386+1)/gcd(953+1,22-1)
(1814*22^10330+1)/gcd(1814+1,22-1)
(953*22^12661+1)/gcd(953+1,22-1)

R22:

(763*22^1023-1)/gcd(763-1,22-1)
(355*22^1051-1)/gcd(355-1,22-1)
(355*22^1143-1)/gcd(355-1,22-1)
(1483*22^1214-1)/gcd(1483-1,22-1)
(2276*22^1342-1)/gcd(2276-1,22-1)
(436*22^1746-1)/gcd(436-1,22-1)
(2536*22^1766-1)/gcd(2536-1,22-1)
(574*22^1800-1)/gcd(574-1,22-1)
(2623*22^1947-1)/gcd(2623-1,22-1)
(997*22^2358-1)/gcd(997-1,22-1)
(697*22^2472-1)/gcd(697-1,22-1)
(1588*22^2487-1)/gcd(1588-1,22-1)
(697*22^2626-1)/gcd(697-1,22-1)
(1732*22^2718-1)/gcd(1732-1,22-1)
(1588*22^2787-1)/gcd(1588-1,22-1)
(2623*22^2955-1)/gcd(2623-1,22-1)
(355*22^3073-1)/gcd(355-1,22-1)
(2230*22^3236-1)/gcd(2230-1,22-1)
(2116*22^3371-1)/gcd(2116-1,22-1)
(997*22^3390-1)/gcd(997-1,22-1)
(697*22^3790-1)/gcd(697-1,22-1)
(1588*22^4035-1)/gcd(1588-1,22-1)
(2276*22^4270-1)/gcd(2276-1,22-1)
(883*22^5339-1)/gcd(883-1,22-1)
(355*22^6408-1)/gcd(355-1,22-1)
(355*22^6543-1)/gcd(355-1,22-1)
(2116*22^6617-1)/gcd(2116-1,22-1)
(2623*22^6987-1)/gcd(2623-1,22-1)
(883*22^7447-1)/gcd(883-1,22-1)
(2083*22^8046-1)/gcd(2083-1,22-1)
(763*22^8616-1)/gcd(763-1,22-1)
(1588*22^9543-1)/gcd(1588-1,22-1)
(2719*22^9671-1)/gcd(2719-1,22-1)
(2623*22^9891-1)/gcd(2623-1,22-1)

S28:

(3566*28^1091+1)/gcd(3566+1,28-1)
(494*28^1594+1)/gcd(494+1,28-1)
(1364*28^2074+1)/gcd(1364+1,28-1)
(1364*28^2110+1)/gcd(1364+1,28-1)
(1043*28^5459+1)/gcd(1043+1,28-1)
(1565*28^8607+1)/gcd(1565+1,28-1)
(1364*28^14418+1)/gcd(1364+1,28-1)

R28:

(1159*28^1036-1)/gcd(1159-1,28-1)
(472*28^2414-1)/gcd(472-1,28-1)
(1507*28^2938-1)/gcd(1507-1,28-1)
(472*28^3954-1)/gcd(472-1,28-1)
(2464*28^4324-1)/gcd(2464-1,28-1)
(1159*28^4956-1)/gcd(1159-1,28-1)
(460*28^5400-1)/gcd(460-1,28-1)
(472*28^5718-1)/gcd(472-1,28-1)
(472*28^7059-1)/gcd(472-1,28-1)
(3019*28^7073-1)/gcd(3019-1,28-1)
(460*28^8121-1)/gcd(460-1,28-1)
(1159*28^8536-1)/gcd(1159-1,28-1)
(3232*28^9147-1)/gcd(3232-1,28-1)
(460*28^9210-1)/gcd(460-1,28-1)
(1507*28^10390-1)/gcd(1507-1,28-1)
(460*28^10718-1)/gcd(460-1,28-1)
(472*28^11474-1)/gcd(472-1,28-1)
(460*28^13548-1)/gcd(460-1,28-1)

[QUOTE=sweety439;488143]Now these (probable) primes are found:

S22:

(1343*22^1878+1)/gcd(1343+1,22-1)
(464*22^2082+1)/gcd(464+1,22-1)
(1814*22^2859+1)/gcd(1814+1,22-1)
(464*22^3634+1)/gcd(464+1,22-1)
(1161*22^3720+1)/gcd(1161+1,22-1)
(1161*22^3897+1)/gcd(1161+1,22-1)
(1793*22^4121+1)/gcd(1793+1,22-1)
(953*22^5596+1)/gcd(953+1,22-1)
(464*22^5794+1)/gcd(464+1,22-1)
(1343*22^7020+1)/gcd(1343+1,22-1)
(953*22^8386+1)/gcd(953+1,22-1)
(1814*22^10330+1)/gcd(1814+1,22-1)
(953*22^12661+1)/gcd(953+1,22-1)

R22:

(763*22^1023-1)/gcd(763-1,22-1)
(355*22^1051-1)/gcd(355-1,22-1)
(355*22^1143-1)/gcd(355-1,22-1)
(1483*22^1214-1)/gcd(1483-1,22-1)
(2276*22^1342-1)/gcd(2276-1,22-1)
(436*22^1746-1)/gcd(436-1,22-1)
(2536*22^1766-1)/gcd(2536-1,22-1)
(574*22^1800-1)/gcd(574-1,22-1)
(2623*22^1947-1)/gcd(2623-1,22-1)
(997*22^2358-1)/gcd(997-1,22-1)
(697*22^2472-1)/gcd(697-1,22-1)
(1588*22^2487-1)/gcd(1588-1,22-1)
(697*22^2626-1)/gcd(697-1,22-1)
(1732*22^2718-1)/gcd(1732-1,22-1)
(1588*22^2787-1)/gcd(1588-1,22-1)
(2623*22^2955-1)/gcd(2623-1,22-1)
(355*22^3073-1)/gcd(355-1,22-1)
(2230*22^3236-1)/gcd(2230-1,22-1)
(2116*22^3371-1)/gcd(2116-1,22-1)
(997*22^3390-1)/gcd(997-1,22-1)
(697*22^3790-1)/gcd(697-1,22-1)
(1588*22^4035-1)/gcd(1588-1,22-1)
(2276*22^4270-1)/gcd(2276-1,22-1)
(883*22^5339-1)/gcd(883-1,22-1)
(355*22^6408-1)/gcd(355-1,22-1)
(355*22^6543-1)/gcd(355-1,22-1)
(2116*22^6617-1)/gcd(2116-1,22-1)
(2623*22^6987-1)/gcd(2623-1,22-1)
(883*22^7447-1)/gcd(883-1,22-1)
(2083*22^8046-1)/gcd(2083-1,22-1)
(763*22^8616-1)/gcd(763-1,22-1)
(1588*22^9543-1)/gcd(1588-1,22-1)
(2719*22^9671-1)/gcd(2719-1,22-1)
(2623*22^9891-1)/gcd(2623-1,22-1)

S28:

(3566*28^1091+1)/gcd(3566+1,28-1)
(494*28^1594+1)/gcd(494+1,28-1)
(1364*28^2074+1)/gcd(1364+1,28-1)
(1364*28^2110+1)/gcd(1364+1,28-1)
(1043*28^5459+1)/gcd(1043+1,28-1)
(1565*28^8607+1)/gcd(1565+1,28-1)
(1364*28^14418+1)/gcd(1364+1,28-1)

R28:

(1159*28^1036-1)/gcd(1159-1,28-1)
(472*28^2414-1)/gcd(472-1,28-1)
(1507*28^2938-1)/gcd(1507-1,28-1)
(472*28^3954-1)/gcd(472-1,28-1)
(2464*28^4324-1)/gcd(2464-1,28-1)
(1159*28^4956-1)/gcd(1159-1,28-1)
(460*28^5400-1)/gcd(460-1,28-1)
(472*28^5718-1)/gcd(472-1,28-1)
(472*28^7059-1)/gcd(472-1,28-1)
(3019*28^7073-1)/gcd(3019-1,28-1)
(460*28^8121-1)/gcd(460-1,28-1)
(1159*28^8536-1)/gcd(1159-1,28-1)
(3232*28^9147-1)/gcd(3232-1,28-1)
(460*28^9210-1)/gcd(460-1,28-1)
(1507*28^10390-1)/gcd(1507-1,28-1)
(460*28^10718-1)/gcd(460-1,28-1)
(472*28^11474-1)/gcd(472-1,28-1)
(460*28^13548-1)/gcd(460-1,28-1)[/QUOTE]

The only new (probable) prime for the k's have no smaller (probable) prime is (2719*22^9671-1)/3.

[QUOTE=sweety439;488143]Now these (probable) primes are found:

S22:

(1343*22^1878+1)/gcd(1343+1,22-1)
(464*22^2082+1)/gcd(464+1,22-1)
(1814*22^2859+1)/gcd(1814+1,22-1)
(464*22^3634+1)/gcd(464+1,22-1)
(1161*22^3720+1)/gcd(1161+1,22-1)
(1161*22^3897+1)/gcd(1161+1,22-1)
(1793*22^4121+1)/gcd(1793+1,22-1)
(953*22^5596+1)/gcd(953+1,22-1)
(464*22^5794+1)/gcd(464+1,22-1)
(1343*22^7020+1)/gcd(1343+1,22-1)
(953*22^8386+1)/gcd(953+1,22-1)
(1814*22^10330+1)/gcd(1814+1,22-1)
(953*22^12661+1)/gcd(953+1,22-1)

R22:

(763*22^1023-1)/gcd(763-1,22-1)
(355*22^1051-1)/gcd(355-1,22-1)
(355*22^1143-1)/gcd(355-1,22-1)
(1483*22^1214-1)/gcd(1483-1,22-1)
(2276*22^1342-1)/gcd(2276-1,22-1)
(436*22^1746-1)/gcd(436-1,22-1)
(2536*22^1766-1)/gcd(2536-1,22-1)
(574*22^1800-1)/gcd(574-1,22-1)
(2623*22^1947-1)/gcd(2623-1,22-1)
(997*22^2358-1)/gcd(997-1,22-1)
(697*22^2472-1)/gcd(697-1,22-1)
(1588*22^2487-1)/gcd(1588-1,22-1)
(697*22^2626-1)/gcd(697-1,22-1)
(1732*22^2718-1)/gcd(1732-1,22-1)
(1588*22^2787-1)/gcd(1588-1,22-1)
(2623*22^2955-1)/gcd(2623-1,22-1)
(355*22^3073-1)/gcd(355-1,22-1)
(2230*22^3236-1)/gcd(2230-1,22-1)
(2116*22^3371-1)/gcd(2116-1,22-1)
(997*22^3390-1)/gcd(997-1,22-1)
(697*22^3790-1)/gcd(697-1,22-1)
(1588*22^4035-1)/gcd(1588-1,22-1)
(2276*22^4270-1)/gcd(2276-1,22-1)
(883*22^5339-1)/gcd(883-1,22-1)
(355*22^6408-1)/gcd(355-1,22-1)
(355*22^6543-1)/gcd(355-1,22-1)
(2116*22^6617-1)/gcd(2116-1,22-1)
(2623*22^6987-1)/gcd(2623-1,22-1)
(883*22^7447-1)/gcd(883-1,22-1)
(2083*22^8046-1)/gcd(2083-1,22-1)
(763*22^8616-1)/gcd(763-1,22-1)
(1588*22^9543-1)/gcd(1588-1,22-1)
(2719*22^9671-1)/gcd(2719-1,22-1)
(2623*22^9891-1)/gcd(2623-1,22-1)

S28:

(3566*28^1091+1)/gcd(3566+1,28-1)
(494*28^1594+1)/gcd(494+1,28-1)
(1364*28^2074+1)/gcd(1364+1,28-1)
(1364*28^2110+1)/gcd(1364+1,28-1)
(1043*28^5459+1)/gcd(1043+1,28-1)
(1565*28^8607+1)/gcd(1565+1,28-1)
(1364*28^14418+1)/gcd(1364+1,28-1)

R28:

(1159*28^1036-1)/gcd(1159-1,28-1)
(472*28^2414-1)/gcd(472-1,28-1)
(1507*28^2938-1)/gcd(1507-1,28-1)
(472*28^3954-1)/gcd(472-1,28-1)
(2464*28^4324-1)/gcd(2464-1,28-1)
(1159*28^4956-1)/gcd(1159-1,28-1)
(460*28^5400-1)/gcd(460-1,28-1)
(472*28^5718-1)/gcd(472-1,28-1)
(472*28^7059-1)/gcd(472-1,28-1)
(3019*28^7073-1)/gcd(3019-1,28-1)
(460*28^8121-1)/gcd(460-1,28-1)
(1159*28^8536-1)/gcd(1159-1,28-1)
(3232*28^9147-1)/gcd(3232-1,28-1)
(460*28^9210-1)/gcd(460-1,28-1)
(1507*28^10390-1)/gcd(1507-1,28-1)
(460*28^10718-1)/gcd(460-1,28-1)
(472*28^11474-1)/gcd(472-1,28-1)
(460*28^13548-1)/gcd(460-1,28-1)[/QUOTE]

Test limits:

S22 at n=14839
R22 at n=11443
S28 at n=22535
R28 at n=18225

[QUOTE=sweety439;488145]Test limits:

S22 at n=14839
R22 at n=11443
S28 at n=22535
R28 at n=18225[/QUOTE]

(Probable) primes found:

(1814*22^16219+1)/gcd(1814+1,22-1)
(883*22^12106-1)/gcd(883-1,22-1)
(2623*22^12211-1)/gcd(2623-1,22-1)
(2536*22^12674-1)/gcd(2536-1,22-1)

Update files for the 1st, 2nd and 3rd conjecture for SR32 and SR64.

S32 has k=4 and k=16 remain, R32 has k=29 remain, SR64 are both proven.

[QUOTE=sweety439;488502](Probable) primes found:

(1814*22^16219+1)/gcd(1814+1,22-1)
(883*22^12106-1)/gcd(883-1,22-1)
(2623*22^12211-1)/gcd(2623-1,22-1)
(2536*22^12674-1)/gcd(2536-1,22-1)[/QUOTE]

(Probable) primes found:

(461*22^16620+1)/gcd(461+1,22-1)
(1364*28^14418+1)/gcd(1364+1,28-1)
(1507*28^20170-1)/gcd(1507-1,28-1)

R36 is fully done, tested to n=1K.

Reserve SR40 and SR52, all bases b<=64 will be done after these reserves were done :smile::smile::smile:

[QUOTE=sweety439;488566]R36 is fully done, tested to n=1K.

Reserve SR40 and SR52, all bases b<=64 will be done after these reserves were done :smile::smile::smile:[/QUOTE]

Update the full R36 file.

[QUOTE=sweety439;488566]R36 is fully done, tested to n=1K.

Reserve SR40 and SR52, all bases b<=64 will be done after these reserves were done :smile::smile::smile:[/QUOTE]

Update files for SR40 and SR52. (tested to n=1K)

Update files for some bases.

Reserve SR78 and SR96, only test the k's not in CRUS.