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sweety439 2022-03-23 19:04

[QUOTE=rudy235;602302]2[SUP]11213[/SUP]-1 would _not_ use BLS or CHG for N-1 as in this case LL is quicker. On the other hand[B] R[/B][SUB]1031[/SUB] was proven by a procedure similar to BLS [FONT="Fixedsys"]Brillhart-Lehmer-Selfridge[/FONT]

See [URL="https://www.ams.org/journals/mcom/1986-47-176/S0025-5718-1986-0856714-3/S0025-5718-1986-0856714-3.pdf"]https://www.ams.org/journals/mcom/1986-47-176/S0025-5718-1986-0856714-3/S0025-5718-1986-0856714-3.pdf[/URL][/QUOTE]

Well ....

k*b^n+1 for b not power of 2 and b^n > k: Pocklington [URL="https://primes.utm.edu/prove/prove3_1.html"]N-1 primality test[/URL]
k*2^n+1 for k not power of 2 and 2^n > k: [URL="https://en.wikipedia.org/wiki/Proth%27s_theorem"]Proth primality test[/URL]
2^n+1: [URL="https://en.wikipedia.org/wiki/P%C3%A9pin%27s_test"]Pépin primality test[/URL] for Fermat numbers

k*b^n-1 for b not power of 2 and b^n > k: Morrison [URL="https://primes.utm.edu/prove/prove3_2.html"]N+1 primality test[/URL]
k*2^n-1 for k not power of 2 and 2^n > k: [URL="https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer%E2%80%93Riesel_test"]Lucas–Lehmer–Riesel primality test[/URL]
2^n-1: [URL="https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test"]Lucas–Lehmer primality test[/URL] for Mersenne numbers

sweety439 2022-05-07 08:51

Predict the smallest integer n such that 67607*2^n+1 is prime
 
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 2022-05-07 10:06

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

[url]https://www.reddit.com/r/Jokes/comments/9gox5r/blonde_50_chance_to_meet_a_dinosaur/[/url]

LaurV 2022-05-11 07:45

[QUOTE=Batalov;605407]Are you, perhaps, a blonde?[/QUOTE]
That is nothing "blonde" in that, as the question is asked, the chances are indeed 50%.

:razz:

sweety439 2022-05-21 08:14

[QUOTE=mart_r;606114]So when will R86453 be verified? :popcorn:[/QUOTE]

When will [URL="http://factordb.com/index.php?id=1100000000490878060"]8*13^32020+183[/URL] (the largest [URL="https://primes.utm.edu/glossary/xpage/MinimalPrime.html"]minimal prime[/URL] in base 13, see [URL="https://github.com/curtisbright/mepn-data/blob/master/data/minimal.13.txt"]https://github.com/curtisbright/mepn-data/blob/master/data/minimal.13.txt[/URL] and [URL="https://cs.uwaterloo.ca/~cbright/reports/mepn.pdf"]https://cs.uwaterloo.ca/~cbright/reports/mepn.pdf[/URL]) be verified? Also see [URL="https://cbright.myweb.cs.uwindsor.ca/reports/cs662-problem12.pdf"]this article[/URL].

(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 2022-05-21 08:46

[QUOTE=frmky;606125](3602,2577) and (3646,2389) are done and uploaded. (3543,3052) is running now.[/QUOTE]

Can you prove the primality of these PRPs which are in order to prove the [URL="https://docs.google.com/document/d/e/2PACX-1vRIjefeGFY7nLpTYSns3JP-aYWGb-4_manLoe1byWwzKmYEW147JaHaC0SfyHF7mwvK29FgpcOr1XfA/pub"]Riesel[/URL] and [URL="https://docs.google.com/document/d/e/2PACX-1vTTLkSb4eY0H19p109lzHjhc-D56gqD9WxyyfQgx_3IEsm2JuA9-cTi1ysy-ahe7RNmc4b9OKKSpYh0/pub"]Sierpinski[/URL] 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 [URL="http://www.fermatquotient.com/PrimSerien/GenRepu.txt"]http://www.fermatquotient.com/PrimSerien/GenRepu.txt[/URL])
* b^n+1 for even b (see [URL="http://jeppesn.dk/generalized-fermat.html"]http://jeppesn.dk/generalized-fermat.html[/URL])
* (b^n+1)/2 for odd b (see [URL="http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt"]http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt[/URL])
* k*b^n+1 ([URL="http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm"]Sierpinski conjecture base b[/URL])
* k*b^n-1 ([URL="http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm"]Riesel conjecture base b[/URL])

etc.

xilman 2022-05-21 10:20

[QUOTE=sweety439;606196]Can you prove the primality of these PRPs which are in order to prove the [URL="https://docs.google.com/document/d/e/2PACX-1vRIjefeGFY7nLpTYSns3JP-aYWGb-4_manLoe1byWwzKmYEW147JaHaC0SfyHF7mwvK29FgpcOr1XfA/pub"]Riesel[/URL] and [URL="https://docs.google.com/document/d/e/2PACX-1vTTLkSb4eY0H19p109lzHjhc-D56gqD9WxyyfQgx_3IEsm2JuA9-cTi1ysy-ahe7RNmc4b9OKKSpYh0/pub"]Sierpinski[/URL] 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 [URL="http://www.fermatquotient.com/PrimSerien/GenRepu.txt"]http://www.fermatquotient.com/PrimSerien/GenRepu.txt[/URL])
* b^n+1 for even b (see [URL="http://jeppesn.dk/generalized-fermat.html"]http://jeppesn.dk/generalized-fermat.html[/URL])
* (b^n+1)/2 for odd b (see [URL="http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt"]http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt[/URL])
* k*b^n+1 ([URL="http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm"]Sierpinski conjecture base b[/URL])
* k*b^n-1 ([URL="http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm"]Riesel conjecture base b[/URL])

etc.[/QUOTE]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 2022-05-21 12:23

[QUOTE=sweety439;606194]When will [URL="http://factordb.com/index.php?id=1100000000490878060"]8*13^32020+183[/URL] (the largest [URL="https://primes.utm.edu/glossary/xpage/MinimalPrime.html"]minimal prime[/URL] in base 13, see [URL="https://github.com/curtisbright/mepn-data/blob/master/data/minimal.13.txt"]https://github.com/curtisbright/mepn-data/blob/master/data/minimal.13.txt[/URL] and [URL="https://cs.uwaterloo.ca/~cbright/reports/mepn.pdf"]https://cs.uwaterloo.ca/~cbright/reports/mepn.pdf[/URL]) be verified? Also see [URL="https://cbright.myweb.cs.uwindsor.ca/reports/cs662-problem12.pdf"]this article[/URL].

(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)[/QUOTE]

@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? :rant:

xilman 2022-05-21 13:03

[QUOTE=paulunderwood;606206]@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? :rant:[/QUOTE]No-one is ever stuck with Windows.

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

mathwiz 2022-05-21 22:29

[QUOTE=sweety439;606196]Can you prove the primality of these PRPs[/QUOTE]

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

chalsall 2022-05-21 23:01

[QUOTE=xilman;606207]No-one is ever stuck with Windows. As well as the WSL solution it is always possible to dual-boot a system.[/QUOTE]

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...


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