Changes to srsieve2

[gd_barnes]

Originally Posted by rogue

Question. If k*b^n+c is not evenly divisible by d, should those terms removed prior to sieving?

Yes.

[henryzz]

Originally Posted by gd_barnes

Yes.

Maybe with a warning but yes. It may be deliberate it may be due to a mistake.

[rogue]

Originally Posted by henryzz

Maybe with a warning but yes. It may be deliberate it may be due to a mistake.

Are you thinking that srsieve2 could output a message like "xxx terms for sequence k*b^n+c are not divisible by d and have been removed"?

[henryzz]

Originally Posted by rogue

Are you thinking that srsieve2 could output a message like "xxx terms for sequence k*b^n+c are not divisible by d and have been removed"?

Yes that could make sense.

[gd_barnes]

Agreed

[sweety439]

Is srsieve2 updated? If so, can you use it to reserve the S3 problem in Sierpinski conjectures and proofs and the R43 problem in Riesel conjectures and proofs? (the latter is a 1k base and I have already used PARI to search it to 12K with no (probable) prime found)

[rogue]

I have not made the change. Too busy.

[sweety439]

Originally Posted by rogue

I have not made the change. Too busy.

See the edit https://github.com/curtisbright/mepn...914128b3303960 in GitHub, you can just remove srsieve divisible by 2 check.

[sweety439]

By the way, this removing is original used for solving the "minimal prime problem" for odd bases, in 2015, a mega-digit (probable) prime (106*23^800873-7)/11 (which is 9{E_800873} in base 23, and the largest minimal prime in base 23) was found to solve the "minimal prime problem" in base 23 (see PRP top link), if one allows probable primes in place of proven primes.

The "minimal prime problem" is solved only for bases 2~16, 18, 20, 22~24, 30, 42, bases <=30 are still reserving (see https://github.com/curtisbright/mepn...ee/master/data, like the CRUS reserving for unproven Sierpinski/Riesel problems) and currently at width 200K and above, but bases 31~50 (see https://github.com/RaymondDevillers/primes) are currently only at width 10K, you can also reserve them like the CRUS reserving.

Note: There are some minimal prime for base 31~50 with width > 10K found by CRUS:

Base 37: (families FY{a} and R8{a} can be removed)

590*37^22021-1 (= FY{a_22021})
1008*37^20895-1 (= R8{a_20895})

Base 45: (families O{0}1 and AO{0}1 can be removed, and hence families O{0}1F1, O{0}ZZ1, unless they have small (probable) prime)

24*45^18522+1 (= O{0_18521}1)
474*45^44791+1 (= AO{0_44790}1) [this prime is not minimal prime]

Base 49: (families 11c{0}1, Fd{0}1, SL{m} and Yd{m} can be removed, and hence families S6L{m}, YUUd{m}, YUd{m}, unless they have small (probable) prime)

2488*49^29737+1 (= 11c{0_29736}1)
774*49^18341+1 (= Fd{0_18340}1)
1394*49^52698-1 (= SL{m_52698})
1706*49^16337-1 (= Yd{m_16337})

Also, I have found a minimal prime with width > 10K in base 40:

(13998*40^12381+29)/13, which equals Qa{U_12380}X in base 40 (the only other unsolved family in base 40 (S{Q}d (86*40^n+37)/3) was tested by me to width 87437, no (probable) prime found