Off-topic

[sweety439]

Originally Posted by rudy235

2¹¹²¹³-1 would _not_ use BLS or CHG for N-1 as in this case LL is quicker. On the other hand R₁₀₃₁ was proven by a procedure similar to BLS Brillhart-Lehmer-Selfridge

See https://www.ams.org/journals/mcom/19...-0856714-3.pdf

Well ....

k*b^n+1 for b not power of 2 and b^n > k: Pocklington N-1 primality test
k*2^n+1 for k not power of 2 and 2^n > k: Proth primality test
2^n+1: Pépin primality test for Fermat numbers

k*b^n-1 for b not power of 2 and b^n > k: Morrison N+1 primality test
k*2^n-1 for k not power of 2 and 2^n > k: Lucas–Lehmer–Riesel primality test
2^n-1: Lucas–Lehmer primality test for Mersenne numbers

[sweety439]

Sierpinski conjectured that 78557 is the smallest odd k such that k*2^n+1 is composite for all integer n (for k = 78557, k*2^n+1 must be divisible by at least one of {3, 5, 7, 13, 19, 37, 73}, thus cannot be prime), and so far, all but 5 smaller odd k have a known prime of the form k*2^n+1, these 5 odd k with no known prime of the form k*2^n+1 are {21181, 22699, 24737, 55459, 67607}, and for these 5 k-values, 67607 has the lowest Nash weight, and thus I think that 67607 has the largest first prime of the form k*2^n+1 among these 5 k-values (and hence also among all odd k-values smaller than 78557), so, let's guess the range of the n for k = 67607

(currently, 67607*2^n+1 has been tested to 36M (> 2^25) without primes found, thus n < 2^25 is impossible)

[Batalov]

Predict based on what? Are you, perhaps, a blonde?

https://www.reddit.com/r/Jokes/comme...et_a_dinosaur/

[LaurV]

Originally Posted by Batalov

Are you, perhaps, a blonde?

That is nothing "blonde" in that, as the question is asked, the chances are indeed 50%.

[sweety439]

Originally Posted by mart_r

So when will R86453 be verified?

When will 8*13^32020+183 (the largest minimal prime in base 13, see https://github.com/curtisbright/mepn...minimal.13.txt and https://cs.uwaterloo.ca/~cbright/reports/mepn.pdf) be verified? Also see this article.

(if this number is verified, then we will complete the classification of the minimal elements of the primes in base 13, since all other minimal primes in base 13 are < 10^345, thus easily to be proven primes)

[sweety439]

Originally Posted by frmky

(3602,2577) and (3646,2389) are done and uploaded. (3543,3052) is running now.

Can you prove the primality of these PRPs which are in order to prove the Riesel and Sierpinski conjecture?

* (79*73^9339-1)/6 (R73)
* (27*91^5048-1)/2 (R91)
* (133*100^5496-1)/33 (R100)
* (3*107^4900-1)/2 (R107)
* (27*135^3250-1)/2 (R135)
* (201*141^5279-1)/20 (R141)
* (1*174^3251-1)/173 (R174)
* (11*175^3048-1)/2 (R175)
* (191*105^5045+1)/8 (S105)
* (11*256^5702+1)/3 (S256)

Except the first and the last of these, they are smaller than your 3543^3052+3052^3543

I think they are more interesting than Leyland numbers, since they are of the form (a*b^n+c)/gcd(a+c,b-1) (with a>=1, b>=2, c != 0, gcd(a,c) = 1, gcd(b,c) = 1), this includes the classic sequences:

* Mersenne numbers 2^n-1
* 2^n+1
* k*2^n-1
* k*2^n+1
* Generalized repunits in base b: (b^n-1)/(b-1) (see http://www.fermatquotient.com/PrimSerien/GenRepu.txt)
* b^n+1 for even b (see http://jeppesn.dk/generalized-fermat.html)
* (b^n+1)/2 for odd b (see http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt)
* k*b^n+1 (Sierpinski conjecture base b)
* k*b^n-1 (Riesel conjecture base b)

etc.

[xilman]

Originally Posted by sweety439

Can you prove the primality of these PRPs which are in order to prove the Riesel and Sierpinski conjecture?

* (79*73^9339-1)/6 (R73)
* (27*91^5048-1)/2 (R91)
* (133*100^5496-1)/33 (R100)
* (3*107^4900-1)/2 (R107)
* (27*135^3250-1)/2 (R135)
* (201*141^5279-1)/20 (R141)
* (1*174^3251-1)/173 (R174)
* (11*175^3048-1)/2 (R175)
* (191*105^5045+1)/8 (S105)
* (11*256^5702+1)/3 (S256)

Except the first and the last of these, they are smaller than your 3543^3052+3052^3543

I think they are more interesting than Leyland numbers, since they are of the form (a*b^n+c)/gcd(a+c,b-1) (with a>=1, b>=2, c != 0, gcd(a,c) = 1, gcd(b,c) = 1), this includes the classic sequences:

* Mersenne numbers 2^n-1
* 2^n+1
* k*2^n-1
* k*2^n+1
* Generalized repunits in base b: (b^n-1)/(b-1) (see http://www.fermatquotient.com/PrimSerien/GenRepu.txt)
* b^n+1 for even b (see http://jeppesn.dk/generalized-fermat.html)
* (b^n+1)/2 for odd b (see http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt)
* k*b^n+1 (Sierpinski conjecture base b)
* k*b^n-1 (Riesel conjecture base b)

etc.

Why not prove them yourself?

I found it very easy to get ecpp-mpi running. It is now churning away on one of my systems which is testing 45986-bit PRP. At 45618 bits the last of your list is smaller than the one I am running so it should not be too difficult for your resources.

[paulunderwood]

Originally Posted by sweety439

When will 8*13^32020+183 (the largest minimal prime in base 13, see https://github.com/curtisbright/mepn...minimal.13.txt and https://cs.uwaterloo.ca/~cbright/reports/mepn.pdf) be verified? Also see this article.

(if this number is verified, then we will complete the classification of the minimal elements of the primes in base 13, since all other minimal primes in base 13 are < 10^345, thus easily to be proven primes)

@sweety439. This seems to be a regular question from you: "when will someone prove...". You really need to get FastECPP running on your system, even if you are stuck with Windows; Simple download and install WSL2. Then you can install and run Linux Ubuntu in the WSL2 virtual system. From there you will have download some packages like openmpi, build-essential, pari-dev, gmp-dev and whatever is required by CM (FastECPP). Et voila, you'll be able to prove some numbers prime. What inhibits you from doing all this?

[xilman]

Originally Posted by paulunderwood

@sweety439. This seems to be a regular question from you: "when will someone prove...". You really need to get FastECPP running on your system, even if you are stuck with Windows; Simple download and install WSL2. Then you can install and run Linux Ubuntu in the WSL2 virtual system. From there you will have download some packages like openmpi, build-essential, pari-dev, gmp-dev and whatever is required by CM (FastECPP). Et voila, you'll be able to prove some numbers prime. What inhibits you from doing all this?

No-one is ever stuck with Windows.

As well as the WSL solution it is always possible to dual-boot a system.

[mathwiz]

Originally Posted by sweety439

Can you prove the primality of these PRPs

Stop asking others to do the work for you. Learn to use the tools yourself.

[chalsall]

Originally Posted by xilman

No-one is ever stuck with Windows. As well as the WSL solution it is always possible to dual-boot a system.

Or, even, simply not have WinBlows in the equation at all.

I recently fired a client because I was fed up with dealing with their WinCrows machines self-destructing.

I was very clear that I was more than happy to continue to support their Linux-based backend systems, but I would no longer support their workstations. I gave them several suggestions for those who would be willing to support them; I never abandon a client.

BTW... The client was my girlfriend...