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 sweety439 2022-01-16 17:13

Off-topic

Like [URL="https://homes.cerias.purdue.edu/~ssw/cun/index.html"]Cunningham table[/URL] to various bases, is there any interest to factor the numbers similar to Fibonacci numbers [URL="https://oeis.org/A000045"]A000045[/URL]? e.g. Pell numbers [URL="https://oeis.org/A000129"]A000129[/URL], 3-Fibonacci numbers [URL="https://oeis.org/A006190"]A006190[/URL], 5-Fibonacci numbers [URL="https://oeis.org/A052918"]A052918[/URL], 6-Fibonacci numbers [URL="https://oeis.org/A005668"]A005668[/URL], etc. (Note: 4-Fibonacci numbers [URL="https://oeis.org/A001076"]A001076[/URL] do not need their own table, since their factorization can be converted to the factorization of the Fibonacci numbers: F(4,n) = F(1,3*n)/2, like that the [URL="https://oeis.org/A001597"]perfect power[/URL] bases do not need their own Cunningham table. The k-Fibonacci number do not need their own table if and only if [URL="https://oeis.org/A013946"]A013946[/URL](k) is the same as a previous term, like that b^n+-1 do not need their own Cunningham table if and only if [URL="https://oeis.org/A052410"]A052410[/URL](b) is the same as a previous term)

 sweety439 2022-02-01 06:35

Some sequences like the Motzkin numbers [URL="https://oeis.org/A001006"]A001006[/URL]:

* Fubini numbers [URL="https://oeis.org/A000670"]A000670[/URL]: For n<=12000, a(n) is prime only for n = 2, 3, 5, 7, 9, 13, see [URL="https://oeis.org/A290376"]A290376[/URL]

* Bell numbers [URL="https://oeis.org/A000110"]A000110[/URL]: For n<=100000, a(n) is prime only for n = 2, 3, 7, 13, 42, 55, 2841, see [URL="https://oeis.org/A051130"]A051130[/URL]

* Euler zigzag numbers [URL="https://oeis.org/A000111"]A000111[/URL]: For n<=69574, a(n) is prime only for n = 3, 4, 6, 38, 454, 510, see [URL="https://oeis.org/A103234"]A103234[/URL] (for odd n, a(n) is even, thus the only prime is a(3) = 2)

There are only very few primes in these four sequences, unlike the Fibonacci numbers [URL="https://oeis.org/A000045"]A000045[/URL], the Pell numbers [URL="https://oeis.org/A000129"]A000129[/URL], the Jacobsthal numbers [URL="https://oeis.org/A001045"]A001045[/URL], the Perrin numbers [URL="https://oeis.org/A001608"]A001608[/URL], the Padovan numbers [URL="https://oeis.org/A000931"]A000931[/URL], the Narayana numbers [URL="https://oeis.org/A000930"]A000930[/URL], there are many primes in these six sequences.

[B]Can you find the next Fubini (probable) prime after [URL="https://oeis.org/A000670"]A000670[/URL](13) = 526858348381?[/B]

 mathwiz 2022-02-01 18:04

[QUOTE=sweety439;599188][B]Can you find the next Fubini (probable) prime after [URL="https://oeis.org/A000670"]A000670[/URL](13) = 526858348381?[/B][/QUOTE]

Why are you asking us? If you're interested, why don't you search for them?

 Uncwilly 2022-02-01 19:52

[QUOTE=mathwiz;599217]Why are you asking us? If you're interested, why don't you search for them?[/QUOTE]
You are free to ignore any posts in this subforum. It will make your life easier.

 tuckerkao 2022-02-04 05:50

[QUOTE=mathwiz;599217]Why are you asking us? If you're interested, why don't you search for them?[/QUOTE]
This thread is under Blogorrhea which has been more of the personal space granted to sweety439, just in case you don't know, sweety439 also enjoys to play around the dozenal math stuffs.

 Batalov 2022-02-04 06:40

[QUOTE=tuckerkao;599353]This thread is under Blogorrhea ...[/QUOTE]
...but he didn't post here.
He posted in completely irrelevant threads - and mods [I](plural![/I]) moved his non-sequiturs here.

 sweety439 2022-02-04 10:58

[QUOTE=charybdis;599348]I don't know if this is the same issue that you were having, but the DB is being flooded. Someone is adding millions of 4x-digit numbers, many of the form 10^46+n, along with their factorizations, and there is now a backlog of millions of unproved small PRPs which is preventing other PRPs from being proved. I've dropped Markus an email. If the user responsible happens to be reading this forum, please could you stop?[/QUOTE]

How to (use bot to) add many numbers in a sequence to factordb? I want to add [URL="https://oeis.org/A000110"]Bell[/URL](n), [URL="https://oeis.org/A000111"]Euler[/URL](n), [URL="https://oeis.org/A000129"]Pell[/URL](n), [URL="https://oeis.org/A000073"]Tribonacci[/URL](n), [URL="https://oeis.org/A006190"]BronzeFibonacci[/URL](n), [URL="https://oeis.org/A000078"]Tetranacci[/URL](n), [URL="https://oeis.org/A001608"]Perrin[/URL](n), [URL="https://oeis.org/A000931"]Padovan[/URL](n), [URL="https://oeis.org/A000930"]Narayana[/URL](n), [URL="https://oeis.org/A000670"]Fubini[/URL](n), [URL="https://oeis.org/A001006"]Motzkin[/URL](n), [URL="https://oeis.org/A007406"]Wolstenholme[/URL](n), [URL="https://oeis.org/A003422"]![/URL](n), [URL="https://oeis.org/A005165"]A[/URL](n), [URL="https://oeis.org/A007489"]K[/URL](n), [URL="https://oeis.org/A000522"]A000522[/URL](n), [URL="https://oeis.org/A000041"]Partition[/URL](n), [URL="https://oeis.org/A000009"]DistinctPartition[/URL](n), [URL="https://oeis.org/A007908"]Sm[/URL](n), [URL="https://oeis.org/A019518"]SmWl[/URL](n), [URL="https://oeis.org/A000422"]RSm[/URL](n), [URL="https://oeis.org/A038394"]RSmWl[/URL](n), and [URL="https://oeis.org/A000521"]A000521[/URL](n) in factordb, for all 1<=n<=10000 (Sm(n) and SmWl(n) and RSm(n) and RSmWl(n) include their analog in bases 2<=b<=36), also the first n digits for many mathematical constants (pi, e, gamma, sqrt(2), ln(2), golden ratio, ...) in bases 2<=b<=36 for all 1<=n<=10000

(I try to use [URL="https://www.tohodo.com/autofill/form.html"]Autofill[/URL] for this, but no success, for the options, I selected "JavaScript" for type and typed these texts for value:

[CODE]
var x = document.querySelector('input[name="query"]');
x.value = '123';
document.querySelector('[type="submit"][value="Factorize!"]').click();

var y = document.querySelector('input[name="query"]');
y.value = '456';
document.querySelector('[type="submit"][value="Factorize!"]').click();

var z = document.querySelector('input[name="query"]');
z.value = '789';
document.querySelector('[type="submit"][value="Factorize!"]').click();
[/CODE]

(I will use PARI/GP program to change "123" and "456" and "789" to the [URL="https://oeis.org/A000110"]Bell numbers[/URL], the [URL="https://oeis.org/A000111"]Euler zigzag numbers[/URL], the [URL="https://oeis.org/A000670"]Fubini numbers[/URL], etc. (my PARI/GP programs can compute them, and can print the codes) also all [URL="http://fatphil.org/maths/rtp/rtp.html"]right-truncatable primes in bases 2<=b<=90[/URL] and all known [URL="https://github.com/RaymondDevillers/primes"]minimal primes in bases 2<=b<=50[/URL] (both datas are available online), and change the variables "x" and "y" and "z" to "x1", "x2", "x3", ...)

but why the factordb only enters 789 to factorize, and does not enter 123 and 456?)

 mathwiz 2022-02-04 21:09

[QUOTE=Uncwilly;599220]You are free to ignore any posts in this subforum. It will make your life easier.[/QUOTE]

The question was honest and non-rhetorical.

I am wondering why OP does not test these sequences {him,her}self. Or, if for a lack of compute resources: why are they important enough that others should test them?

 Uncwilly 2022-02-04 21:20

There are theoretical physics and there are experimental ones. Just maybe the person in question leans to the theoretical end of maths.

 tuckerkao 2022-02-04 23:00

[QUOTE=mathwiz;599404]The question was honest and non-rhetorical.

I am wondering why OP does not test these sequences {him,her}self. Or, if for a lack of compute resources: why are they important enough that others should test them?[/QUOTE]
Sweety439 may just have his own favorite preference digging into certain areas which aren't important to other people at all.

I saw a mechanical product online recently and it showed the product number of 48-53-2837 - [URL="https://www.pinterest.com/pin/501236633550226758/"]https://www.pinterest.com/pin/501236633550226758/[/URL]

So I've decided that I want to run a PRP test of 2[SUP]48,532,837[/SUP] - 1 myself(This exponent is a decimal composite but a dozenal prime with a different interpretation), my reason won't be good enough to convince anyone else, glad I have to plenty computing resources under my roof to finish it without bothering Kriesel again.

 paulunderwood 2022-02-04 23:07

[QUOTE=tuckerkao;599408]

So I've decided that I want to run a PRP test of 2[SUP]48,532,837[/SUP] - 1 myself(This exponent is a decimal composite but a dozenal prime with a different interpretation), my reason won't be good enough to convince anyone else, glad I have to plenty computing resources under my roof.[/QUOTE]

:crank::rakes:

:wrong:

:missingteeth:

 a1call 2022-02-04 23:12

[url]https://www.wolframalpha.com/input?i=48532837_12+to+base+10[/url]

[url]https://www.wolframalpha.com/input?i=168526123+is+prime[/url]

[url]https://www.mersenne.org/report_exponent/?exp_lo=168526123&exp_hi=[/url]

 paulunderwood 2022-02-04 23:19

:redface: I see. Convert to base 10 from base 12. Silly me. Got for it Tucker! No one is stopping you. Good luck!

(I initially thought that T. was saying that converting a prime to another base somehow changed its primeness. Sorry).

 Dobri 2022-02-05 00:16

[QUOTE=tuckerkao;599408]So I've decided that I want to run a PRP test of 2[SUP]48,532,837[/SUP] - 1 myself(This exponent is a decimal composite but a dozenal prime with a different interpretation),...[/QUOTE]
Note that 48,532,837 = 2,281 × 21,277 and two of the factors of (2[SUP]48532837[/SUP] - 1) are (2[SUP]2281[/SUP] - 1) and (2[SUP]21277[/SUP] - 1) where (2[SUP]2281[/SUP] - 1) is the 17th Mersenne prime M[M]2281[/M] and M[M]21277[/M] has a known factor.

 Dobri 2022-02-05 00:53

[QUOTE=tuckerkao;599408]So I've decided that I want to run a PRP test of 2[SUP]48,532,837[/SUP] - 1 myself(This exponent is a decimal composite but a dozenal prime with a different interpretation),...[/QUOTE]
As for 48,532,837[SUB]12[/SUB] = 168,526,123[SUB]10[/SUB], it is a prime number indeed.
Off-topic: [SPOILER]Throughout the Chinese Lunar Year Huangdi (Yellow Emperor) 4720 (2022) of the Water Tiger, lucky numbers allegedly are 1, 3, and 4 as well as numerals that contain them such as 14 and 34. The digit sum of 168,526,123 is 34 and there is no known Mersenne prime having an exponent with said digit sum. :)[/SPOILER]

 sweety439 2022-02-08 05:17

Other than single-digit primes (2, 3, 5, 7), can a Mersenne exponent be a [URL="https://en.wikipedia.org/wiki/Palindromic_prime"]palindromic prime[/URL]?

 kriesel 2022-02-08 19:09

[QUOTE=sweety439;599635]Other than single-digit primes (2, 3, 5, 7), can a Mersenne exponent be a [URL="https://en.wikipedia.org/wiki/Palindromic_prime"]palindromic prime[/URL]?[/QUOTE]For Mersenne numbers, there are ~5172 prime palindromic exponents of 9 decimal digits. Many of them have already been factored or otherwise shown composite. All the shorter palindromic exponent Mersennes have already been tested and found composite. There are no known Mersenne primes with exponent > 10 and palindromic exponent. Primality testing passed above 10[SUP]8[/SUP] a while ago. But the sample size of known Mersenne primes' exponents is small at 51. If the exponent distribution of Mersenne primes is random in some sense, the odds of any of the estimated 6 Mersenne primes remaining to be discovered below 1G exponent having a palindromic exponent are very poor, at ~6 chances, each with odds ~1/4000 of having a palindromic exponent, or roughly 6/4000 overall. p=abcd e dcba would not allow a=2,4,5,6,8, only a=1,3,7,9.
So we already know there are no (base 10) palindromic exponent Mersenne primes between exponents:
11. - 60M & probably to 107M; 200M-300M; 400M-700M; 800M-900M;
leaving 60M likely 107M - 200M, 300M - 400M, 700M - 800M, 900M+.

The odds get worse for 10 or more digit exponents.
[URL]https://www.mersenneforum.org/showpost.php?p=567246&postcount=5[/URL]

Changing bases, there are more. Consider base two. 3, 5, 7, 17, 31, 107, 127.

 chalsall 2022-02-08 19:14

[QUOTE=kriesel;599666]The odds get worse for 10 or more digit exponents.[/QUOTE]

I know it's not easy to do...

But... I keep being told by those I trust that speaking into a vacuum means (by definition) that few actually receive your message.

 Dr Sardonicus 2022-02-08 20:36

[QUOTE=kriesel;599666]<snip>
The odds get worse for 10 or more digit exponents.
<snip>[/QUOTE]If k > 1, the odds of a palindromic number with 2*k digits being prime are [i]zero[/i]. (This is true in any integer base b > 1; the reason is that such numbers are automatically divisible by b + 1, with cofactor automatically greater than 1 if k > 1.)

For positive integer k, the number of 2*k + 1 digit palindromic numbers to base ten is 9*10[sup]k[/sup] (9 possible non-zero digits for the first and last digit, ten possible middle digits, and an arbitrary block of k-1 digits in between).

Of these, 4*10[sup]k[/sup] are relatively prime to 10. Apart from that, I have no idea of the likelihood of a palindromic number of 2*k + 1 decimal digits being prime. Under the "assumption of ignorance" that the likelihood is the same as a random odd number prime to 10, something on the order of 1/(2*k*log(10)) of them would be prime. But the total number of palindromic numbers is tiny compared to the number of primes if k is large.

The number of primes with 2*k + 1 decimal digits is roughly 9*10[sup]2k[/sup]/((2k)*log(10)), so the odds of a 2k+ 1 digit prime being palindromic are less than 8*k*log(10)/9 in 10[sup]k[/sup]. Under the "assumption of ignorance" the odds would be something like 4/9 in 10[sup]k[/sup] (unless I botched the calculation, of course) :grin:

 sweety439 2022-03-21 18:39

R49081 is now proven prime, see post [URL="https://mersenneforum.org/showpost.php?p=602219&postcount=35"]https://mersenneforum.org/showpost.php?p=602219&postcount=35[/URL]

 sweety439 2022-03-22 11:33

[QUOTE=Dr Sardonicus;602253]The University of Illinois used to have a post mark commemorating its achievement finding the latest Mersenne prime, proving that

[color=red]2[sup]11213[/sup] - 1 IS PRIME[/color]

Imagine the possibilities of putting

[b][i][size=+1]R[/size][/i][/b][sub]49081[/sub] IS PRIME

on something :big grin:[/QUOTE]

2^11213-1 can be easily proven prime because its N+1 can be trivially 100% factored:

Pocklington [URL="https://primes.utm.edu/prove/prove3_1.html"]N-1 primality test[/URL] --> [URL="https://en.wikipedia.org/wiki/Proth%27s_theorem"]Proth primality test[/URL] --> [URL="https://en.wikipedia.org/wiki/P%C3%A9pin%27s_test"]Pépin primality test[/URL] for Fermat numbers

Morrison [URL="https://primes.utm.edu/prove/prove3_2.html"]N+1 primality test[/URL] --> [URL="https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer%E2%80%93Riesel_test"]Lucas–Lehmer–Riesel primality test[/URL] --> [URL="https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test"]Lucas–Lehmer primality test[/URL] for Mersenne numbers

However, for R49081, neither N-1 nor N+1 can be trivially >= 33.3333% factored, thus ECPP primality test (such PRIMO) is needed to use, thus they are very different.

See [URL="https://primes.utm.edu/primes/lists/all.txt"]top definitely primes[/URL] and [URL="http://www.primenumbers.net/prptop/prptop.php"]top probable primes[/URL], for the top definitely primes, (usually) one of N-1 and N+1 is trivially 100% factored, while for top probable primes, none of them can be >= 33.3333% factored.

 rudy235 2022-03-22 15:05

[QUOTE=sweety439;602283]2^11213-1 can be easily proven prime because its N+1 can be trivially 100% factored:[/QUOTE]

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]

 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?

 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...

 xilman 2022-05-22 09:31

[QUOTE=chalsall;606225]Or, even, simply not have WinBlows in the equation at all.[/QUOTE]
I withdraw my earlier remark.

There are some unusual systems which appear to require Windows.

The only driver for my observatory dome is exclusively Windows. There doesn't appear to be anything for Linux or MacOS, and I have looked very hard.

It might, just might, run under WINE but I really don't want to put that much effort into something which may not work anyway.

 xilman 2022-05-23 09:46

[QUOTE=xilman;606245]I withdraw my earlier remark.

There are some unusual systems which appear to require Windows.

The only driver for my observatory dome is exclusively Windows. There doesn't appear to be anything for Linux or MacOS, and I have looked very hard.

It might, just might, run under WINE but I really don't want to put that much effort into something which may not work anyway.[/QUOTE]@chasall: I started replying to your response here but realised we were too off-topic even for a thread titled "off-topic".

It seems to be much more appropriate in the [URL="https://mersenneforum.org/showthread.php?t=27813"]Hobbies/Astronomy sub-forum[/URL].

 ryanp 2022-05-23 18:11

[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)[/QUOTE]

I did one of these as a warmup for testing out cm 0.4.1-dev with Paul Underwood's [C]gw_prp[/C] [STRIKE]hack[/STRIKE] enhancement. You should work on the others yourself.

 sweety439 2022-05-28 14:29

Does such repunit exist?

Is there a repunit Rp with p prime, such that 2*p+1 is prime, and Rp/(2*p+1) is also prime, in base 10? In base 2, there are many such p's: {11, 23, 83, 131, 3359, 130439, 406583, ...}, see [URL="https://oeis.org/A239638"]A239638[/URL], also in base 3, there are such p's: {5, 11, 23, 131}, in base 6, the only known such p is 11, but in base 10, I check to 100000 without finding any such prime p, so, is there a prime p such that 2*p+1 is prime, and Rp/(2*p+1) is also prime? (i.e. is there a prime p such that the repunit Rp is a semiprime, and 2*p+1 is a factor of it?)

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