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 pepi37 2019-09-18 16:59

Small but sweet :)
[Worker #1 Sep 18 17:41:47] 9*10^380734+1 is a probable prime! Wh8: 0976AF3D,00000000

And of course it is proven prime with LLR :)

:party:

 rudy235 2020-03-04 03:02

This one has not been yet verified but it looks genuine.

6962 · 31[sup]2863120[/sup] - 1

4269952 Digits. Largest of the year. Will rank 20 if verified.

[url]https://primes.utm.edu/primes/page.php?id=130702[/url]

 paulunderwood 2020-03-13 15:21

Congrats to Ryan Propper for his recent batch of proth mega primes for k = 9, 11 and 13 the largest of which has 3,462,100 digits :smile:

 JeppeSN 2020-03-16 17:13

[QUOTE=paulunderwood;539623]Congrats to Ryan Propper for his recent batch of proth mega primes for k = 9, 11 and 13 the largest of which has 3,462,100 digits :smile:[/QUOTE]

What ranges was Propper searching, and did he keep the residues of all the composite candidates he must have covered? This information could be useful to PrimeGrid which is planning to search and double-check (at least a part of) these Proth number regions, see [URL="https://www.primegrid.com/stats_div_llr.php"]https://www.primegrid.com/stats_div_llr.php[/URL].

/JeppeSN

 paulunderwood 2020-03-16 22:29

[QUOTE=JeppeSN;539859]What ranges was Propper searching, and did he keep the residues of all the composite candidates he must have covered? This information could be useful to PrimeGrid which is planning to search and double-check (at least a part of) these Proth number regions, see [URL="https://www.primegrid.com/stats_div_llr.php"]https://www.primegrid.com/stats_div_llr.php[/URL].

/JeppeSN[/QUOTE]

pm ryanp

 pepi37 2020-03-24 19:15

New near-repdigit prime :)

93*10^642225-1 :)

[URL]https://primes.utm.edu/primes/page.php?id=130796[/URL]

 paulunderwood 2020-03-24 20:09

[QUOTE=pepi37;540770]93*10^642225-1 :)

[URL]https://primes.utm.edu/primes/page.php?id=130796[/URL][/QUOTE]

Congrats!

 pepi37 2020-03-24 20:32

[QUOTE=paulunderwood;540780]Congrats![/QUOTE]

Thanks!

 paulunderwood 2020-03-30 13:04

[QUOTE=paulunderwood;539623]Congrats to Ryan Propper for his recent batch of proth mega primes for k = 9, 11 and 13 the largest of which has 3,462,100 digits :smile:[/QUOTE]

Go, Ryan, go. The latest is 28th biggest known prime with 3,734,847 digits:
[URL="https://primes.utm.edu/primes/page.php?id=130801"]
9*2^12406887+1[/URL]

 JeppeSN 2020-04-01 08:53

[QUOTE=paulunderwood;541322]Go, Ryan, go. The latest is 28th biggest known prime with 3,734,847 digits:
[URL="https://primes.utm.edu/primes/page.php?id=130801"]
9*2^12406887+1[/URL][/QUOTE]

There is already a newer and bigger one, [URL="https://primes.utm.edu/primes/page.php?id=130806"]9*2^13334487 + 1[/URL]. He has found 9 huge Proth primes with k in { 9, 11, 13 } in the month of March.

Ryan Propper does not respond to private messages.

/JeppeSN

 rudy235 2020-06-01 01:38

NOT YET VERIFIED

The largest Generalized Fermat of the Year. (and also the largest of the form a^2[SUP]19[/SUP]+1 )

Congratulations to Wolfang and his team.

3638450[SUP]524288[/SUP] + 1 3439810 L4591 May 31st 2020

Ranked as 35 of the list.

 paulunderwood 2020-06-13 16:10

The 20th largest known prime has been found by Ryan Propper:

[URL="https://primes.utm.edu/primes/page.php?id=130967"]6*5^6546983 + 1[/URL]

:banana:

 pepi37 2020-06-25 21:04

Nice and shiny fresh one

[URL]https://primes.utm.edu/primes/page.php?id=130989[/URL]

9 *10^583696 + 1 :)

 carpetpool 2020-07-06 03:34

This has been my lucky weekend (just yesterday, I found a T5K prime for CRUS):

26*3^1435875+1 may be prime, but N divides 3^((N-1)/3))-1, restarting with a=5 Time : 1308.400 sec.
26*3^1435875+1 is prime! (685088 decimal digits) Time : 1299.598 sec.

 a1call 2020-07-06 06:06

Congratulations [B]carpetpool[/B]. It's good to see that at least some of the Top 5k contributors are nice people.:smile:
Well done!

 carpetpool 2020-07-13 22:48

Another lucky hit:

26*3^1700041+1 may be prime, but N divides 3^((N-1)/3))-1, restarting with a=5 Time : 938.494 sec.
26*3^1700041+1 is prime! (811128 decimal digits) Time : 946.942 sec.

 rudy235 2020-08-01 17:44

Largest prime for 2020 (till now)

TO BE VERIFIED

Congratulations to Serge Batalov.

Gaussian Mersenne. #20 on the current list.

2[SUP]15317227[/SUP] + 2[SUP]7658614[/SUP] + 1

4,610,945 digits.

 pepi37 2020-08-01 20:16

[QUOTE=rudy235;552206]TO BE VERIFIED

Congratulations to Serge Batalov.

Gaussian Mersenne. #20 on the current list.

2[SUP]15317227[/SUP] + 2[SUP]7658614[/SUP] + 1

4,610,945 digits.[/QUOTE]

Serge never publish prime until he is 101% sure it is prime :)

 rudy235 2020-08-02 17:36

[QUOTE=pepi37;552218]Serge never publish prime until he is 101% sure it is prime :)[/QUOTE]

Well, 101 happens to be prime.

 paulunderwood 2020-10-30 22:13

Congrats to Scott Brown for the "321+" prime, [URL="https://primes.utm.edu/primes/page.php?id=131362"]3*2^16408818+1[/URL], which was 6.5 years in the making by PrimeGrid.

:banana:

 kar_bon 2020-11-17 21:06

Seems a new prime for the [url='https://www.rieselprime.de/ziki/Riesel_problem']Riesel Problem[/url] was found: [url='https://primes.utm.edu/primes/page.php?id=131405']146561*2^11280802-1[/url] found by PrimeGrid's project currently in verify status.
This is, when proven, almost 3 years after the last found for this problem.

 paulunderwood 2020-12-01 17:46

"P587124"

Congrats to a1call for [URL="https://primes.utm.edu/primes/page.php?id=131431"]this top5000 prime[/URL] of a most unusual construction.

:banana:

 sweety439 2020-12-01 19:05

[QUOTE=kar_bon;563554]Seems a new prime for the [url='https://www.rieselprime.de/ziki/Riesel_problem']Riesel Problem[/url] was found: [url='https://primes.utm.edu/primes/page.php?id=131405']146561*2^11280802-1[/url] found by PrimeGrid's project currently in verify status.
This is, when proven, almost 3 years after the last found for this problem.[/QUOTE]

this number is now proven to be prime, now there are 47 Riesel base 2 candidate left.

 kar_bon 2020-12-01 23:49

[QUOTE=sweety439;564956]this number is now proven to be prime, now there are 47 Riesel base 2 candidate left.[/QUOTE]

No, that page was already updated: there're still 48 k-values left.

 pepi37 2020-12-11 23:32

New 1.43M repdigit prime will appear soon :)
It was time to find something bigger after 5 years searching in this sequence :)

 Batalov 2020-12-11 23:43

Good! Congratulations!

 pepi37 2020-12-11 23:44

[QUOTE=Batalov;565974]Good! Congratulations![/QUOTE]
Thanks!

 carpetpool 2020-12-12 09:08

[QUOTE=paulunderwood;564951]Congrats to a1call for [URL="https://primes.utm.edu/primes/page.php?id=131431"]this top5000 prime[/URL] of a most unusual construction.

:banana:[/QUOTE]

Very interesting, indeed.

The prime in question does not appear to be totally random?

I have actually constructed large random provable primes before (over 100,000 digits), but none of them were large enough size for Top5000 at the time.

This was a few years ago though and I had lost interest at some point.

I am also wondering how sieving was done. I've made general purpose programs and scripts for my searches in finding random primes, but they are far too slow at half a million digits compared to more advanced programs like srsieve and multisieve which won't support testing arbitrary numbers.

Also, PFGW appears to test some numbers faster than others, like Proth or Riesel numbers, so I could only imagine the extensive work done to find this prime.

These primes also might be of interest:

[url]https://primes.utm.edu/primes/page.php?id=119933[/url]

[url]https://primes.utm.edu/primes/page.php?id=119934[/url]

Edit: I did not see Paul's post was about a week ago, for some reason, this caught my attention...

 pepi37 2020-12-12 12:21

And now it is official :)

[URL="https://primes.utm.edu/primes/page.php?id=131466"]92*10^1439761-1 is prime :)[/URL]

:victor::victor::victor::victor::victor::victor:

 a1call 2020-12-12 20:39

@carpetpool
The prime has taken months of work for different iterations and I have modified the sieving over time.
As per faster PRP tests for some numbers than others of the same size, I believe it's a matter of proximity to repeated squaring which these iterations happen to be. The same behavior can be seen in Pari when calculating Mod (b,p)^(p-1) which is much faster if p is close to repeated squares which indicates that the routines have the intelligence to figure out the fastest way of calculating an Exponentiation.
As for the sieving, I use my own setup which means it is probably quite inefficient. However it has one thing going for it:
There is often the raised subject of how deep to sieve and I generally disagree with the replies.
IMHO one should sieve indefinitely and simultaneously as PRP testing. I basically take a range and let lose multiple threads at sieving it using both PRP-Test-threads and TF-sieving-threads. Any candidate in the queue that is knocked out by TF saves days of upcoming PRP tests.

I have a ryzen 9 PC dedicated to this sequence and run my routines in a virtual box which I can pause, snapshot and resume at any time.
I am currently looking for the next iteration but things have slowed down to a crawl. It appears that PRP tests are about 8 times slower than the last iteration.

ETA Good luck with your next Top-5k carpetpool.:smile:

 bur 2020-12-14 07:05

[QUOTE]IMHO one should sieve indefinitely and simultaneously as PRP testing. I basically take a range and let lose multiple threads at sieving it using both PRP-Test-threads and TF-sieving-threads. Any candidate in the queue that is knocked out by TF saves days of upcoming PRP tests.[/QUOTE]If the same computer doing the sieving could eliminate candidates faster by using PRP, what's the advantage of sieving? Or vice versa.

 a1call 2020-12-14 12:41

Suppose you are testing 10000 candidates with 1M decimal digits each. And each PRP test takes 4 days and you have 10 threads available. Suppose you run PRP tests on 9 of them and trial factoring on the other. In the 1st 4 days anything divisible by small primes will be knocked out by TF. In the next 4 days candidates divisible by larger primes will be knocked out, next 4 days even larger.... Any candidates that are knocked out of the queue at [U]anytime[/U] means you don't have to spend 4 days for a PRP test on them.

 VBCurtis 2020-12-14 16:07

In no way did your explanation answer why sieving is better after the point where a prp test eliminates candidates faster than sieve does. If your sieve eliminates a candidate every 6 days, why do you think you're saving 4 days every time you find a factor?

When sieve is faster, sieve on all 10 threads. When prp is faster, prp on all 10 threads. You way may be convenient for you, but it's not an effort to be efficient.

 a1call 2020-12-14 22:15

Suppose you have 2 available threads.
Suppose there are z candidates to test, none of which are prime.
Suppose each PRP-Test takes 4 days to complete.
Suppose running the 2 TF-threads for 4 days would sieve upto some prime x per thread.
Suppose y of the candidates have prime factors greater than x.
For the sake of the argument let's ignore the time it takes to run the TF-test on all the candidates.
the PRP tests alone will take 4y/2 days.
------
Now suppose you run 1 of the threads for trial-factoring indefinitely which means the candidates upstream the queue will be sieved deeper and deeper than x.
The other thread is used for PRP-tests
It will take you less than 4y days to PRP test all the candidates because some more of the candidates will be knocked out by TF.
How much less days is a factor of how large z is. The larger the z, the deeper the TF, the greater cutdown from 4y days.
Since there is no known upper bound for z, there is always a z value feasible where PRP tests will take less than 4y/2.

That's my 2 cents and that's how I run my setup, but you are welcome to disagree.:smile:

 a1call 2020-12-14 23:41

Couldn't add an ETA.
To make it clearer the 2 scenarios are a bit of apples and oranges comparison. The second scenario sieves less deep in the beginning and more deep towards the end. However its depth has no upper bound unlike the 1st scenario. I hope that makes sense.:smile:

 VBCurtis 2020-12-15 01:10

We understand what you do, so "makes sense" is a pretty low bar. We disagree that it's faster.

Sieve on both threads until it takes longer than 4 days to find a factor. Then prp on both threads. Every candidate is optimally sieved this way, while in your way the first few tests are badly undersieved, and the last few are really badly oversieved.

If we both take a range and race on identical hardware, your way comes out slower. But, if you like the triumph of finding a factor, it's just fine to rank speed as not the first priority. Just don't claim it's better!

 paulunderwood 2021-01-22 02:17

321

Congrats to Rudi Tapper and PrimeGrid for the prime [URL="https://primes.utm.edu/primes/page.php?id=131595"]3* 2^16819291 - 1[/URL] with 5,063,112 decimal digits and top5000 entrance rank of 21.

:banana:

 bur 2021-01-26 07:13

[QUOTE=a1call;566150]Suppose you are testing 10000 candidates with 1M decimal digits each. And each PRP test takes 4 days and you have 10 threads available. Suppose you run PRP tests on 9 of them and trial factoring on the other. In the 1st 4 days anything divisible by small primes will be knocked out by TF. In the next 4 days candidates divisible by larger primes will be knocked out, next 4 days even larger.... Any candidates that are knocked out of the queue at [U]anytime[/U] means you don't have to spend 4 days for a PRP test on them.[/QUOTE]I only saw this now, sorry. Sounds convincing at first, but why not use 2 out of 10 threads, or 7 or all?

Fundamentally you have two methods to remove a candidate for good, TF or PRP. If one is faster on average, you have the highest average throughput when using that method exclusively. I don't see how it can be different.

[QUOTE]Congrats to Rudi Tapper and PrimeGrid for the prime 3* 2^16819291 - 1 with 5,063,112 decimal digits and top5000 entrance rank of 21.[/QUOTE]After 5 days verifying it was finally added to the list.

 a1call 2021-01-26 08:21

[QUOTE=bur;570120]

Fundamentally you have two methods to remove a candidate for good, TF or PRP. If one is faster on average, you have the highest average throughput when using that method exclusively. I don't see how it can be different.

[/QUOTE]

By that logic there would be no justification to use more than one method, either TF or PRP-Testing on any given range. But that's not the case now, is it?
Both methods are used in practice to weed out candidates they are better at sieving. TF for candidates with smaller factors and PRP-Testing for the rest, even though one would have to be faster on acreage on the whole set than the other.

 VBCurtis 2021-01-26 15:24

[QUOTE=a1call;570125]By that logic there would be no justification to use more than one method, either TF or PRP-Testing on any given range. But that's not the case now, is it?
Both methods are used in practice to weed out candidates they are better at sieving. TF for candidates with smaller factors and PRP-Testing for the rest, even though one would have to be faster on acreage on the whole set than the other.[/QUOTE]
No, you are fully misunderstanding what he said.

If TF is faster, use it exclusively. At some point in your TF efforts, TF is no longer faster, and PRP becomes faster. At that crossover point, use PRP exclusively.

This is clearly the most efficient path, yet you wave your hands and use all sorts of words to make yourself feel better that it's not true.

 LaurV 2021-01-27 09:43

[QUOTE=a1call;570125]By that logic there would be no justification to use more than one method, either TF or PRP-Testing on any given range.[/QUOTE]
That's a fallacy. It would be true if the speed of each method would be constant as you go deeper, but it is not. The TF speed decreases exponentially, it halves with every bitlevel. The speed of PRP decreases slower with the size of the exponent (range, size of the FFT). In a certain point they will cross. As VBCurtis says.

By "speed of TF" we mean how fast you can eliminate an exponent, by finding a factor. TF programs seem "much faster", they do many tests in the wallclock time taken by a PRP test, but to find a factor, you need to do many assignments (roughly, equal to the bitlevel, i.e. if you look for 70 bits factors, you will need to test about 70 exponents, to find a factor). If your hardware can test 70 exponents to 70 bits faster than it takes for the same hardware to do a PRP for an exponent of the same size (plus or minus a little change, considering the certification process, error rates, vanity of having a factor as opposite of having a PRP residue, whatever rows your boat), then YOU SHOULD CERTAINLY DO ONLY TF to 70 bits.

This is how GIMPS works since its inception, if we make abstraction of the people who only run TF because they want more credit, or they like to have found factors, or (I would say "selfish") people who only run LL/PRP because they want the glory of finding a prime and take George's money. :razz: Most users here will try to help the project most, by optimizing their rate of getting rid of exponents, at front wave, either doing TF or PRP. Of course, the options will wary in time, according with the exponent size at the front level and the bitlevel that has to be trial-factored, you can do PRP today because the bitlevels are very deep here, and TF next month if your exponent gets higher and the bitlevel is lower or stays the same, but once the exponent and bitlevel is given, and [U]assuming you know your hardware[/U], you should optimally chose ONE of them, and DO THAT ONE ONLY.

 paulunderwood 2021-02-19 08:30

Congrats to Serge Batalov for the smallest known 1 million digit prime:

[URL="https://primes.utm.edu/primes/page.php?id=131964"]10^999999 + 308267*10^292000 + 1[/URL]

Can this be limbo-ed?

 JeppeSN 2021-02-19 08:48

[QUOTE=paulunderwood;571995]Congrats to Serge Batalov for the smallest known 1 million digit prime:

[URL="https://primes.utm.edu/primes/page.php?id=131964"]10^999999 + 308267*10^292000 + 1[/URL]

Can this be limbo-ed?[/QUOTE]

This beats an idea of simply doing 10^999999 + k*10^(333333-m) ± 1 with m very small. Such a prime would be simpler to test than Serge Batalov's, but not quite as close to 10^999999. /JeppeSN

 sweety439 2021-02-19 19:36

[QUOTE=paulunderwood;571995]Congrats to Serge Batalov for the smallest known 1 million digit prime:

[URL="https://primes.utm.edu/primes/page.php?id=131964"]10^999999 + 308267*10^292000 + 1[/URL]

Can this be limbo-ed?[/QUOTE]

The smallest known 1 million digit [STRIKE]prime[/STRIKE] is 10^999999+593499

 paulunderwood 2021-02-19 19:42

[QUOTE=sweety439;572046]The smallest known 1 million digit prime is 10^999999+593499[/QUOTE]

That may be the smallest PRP. No proof of primality, unless you have a new theorem :smile:

 paulunderwood 2021-03-02 18:52

DRUG is PRP top

We had a nice email from Jeff Gilchrist this morning saying one of his computers had reported:

[CODE]2^13380298-27 is base 3-Fermat PRP! (4027872 decimal digits) Time : 9677.550 sec.
2^13380298-27 is Fermat, Lucas and Frobenius PRP! (P = 5, Q = 5, D = 5) Time : 75222.576 sec.
[/CODE]

We would like to thank rouge for his sieve and Jean and George for their software.

:banana: :banana: :banana: :banana:

It is [URL="http://www.primenumbers.net/prptop/prptop.php?page=1"]official now[/URL]

 Batalov 2021-03-11 22:52

A new [URL="https://primes.utm.edu/primes/page.php?id=132142"]Generalized Cullen number[/URL] - 4'143'644 decimal digits.

 pepi37 2021-03-12 21:01

[QUOTE=Batalov;573447]A new [URL="https://primes.utm.edu/primes/page.php?id=132142"]Generalized Cullen number[/URL] - 4'143'644 decimal digits.[/QUOTE]
:bow:

 Batalov 2021-04-20 21:52

DRUG is PRP 2nd top now :wink:

[QUOTE=paulunderwood;572866]We had a nice email from Jeff Gilchrist this morning saying one of his computers had reported:
[C]2^13380298-27 is base 3-Fermat PRP! (4027872 decimal digits) Time : 9677.550 sec.[/c][/QUOTE]
Sorry, Paul, [URL="https://mersenneforum.org/showthread.php?t=26719"]the top is now retaken
[/URL]

 paulunderwood 2021-04-20 22:08

[QUOTE=Batalov;576287]Sorry, Paul, [URL="https://mersenneforum.org/showthread.php?t=26719"]the top is now retaken
[/URL][/QUOTE]

The rep-digit is an admirable find.

 kar_bon 2021-05-27 11:14

Riesel problem

After years of work from [url='https://www.rieselprime.de/ziki/Riesel_Sieve']RieselSieve[/url] and further testing/sieving/double checking by PrimeGrid there are currently [url='http://www.prothsearch.com/rieselprob.html']44 k-values[/url] left for which no prime k*2^n-1 was found yet.
After three primes found by Ryan Propper this year for the [url='https://www.rieselprime.de/ziki/Riesel_problem']Riesel problem[/url] and a [url='https://www.primegrid.com/forum_thread.php?id=9624&nowrap=true#149296']post[/url] from him at the PG forum, which says he's "doing some solo hunting" work for 12M<=n<=15M (but not explicitly given which k-values), PrimeGrid seems stopped the search for those 3 found k-values according to their [url='https://www.primegrid.com/stats_trp_llr.php']status page[/url] showing they stopped checking at n~11.5M.
So this will leave a range of uncertainty if there eventually exists a smaller prime than those found ones.

Open questions:
- Will PG check the missing ranges?
- Is Ryan Propper testing further ranges/k-values? If so, which ones?

Before this is cleared, the Riesel problem still stay at 47 open k-values left to prove the problem and I think neither Wilfrid Keller nor any serious prime hunter will rest until this inconsistency is resolved.

To all: please comunicate your search and make them available to avoid duplicate work.

 Batalov 2021-05-27 18:07

[QUOTE=kar_bon;579200]Before this is cleared, the Riesel problem still stay at [B]47[/B] open k-values left to prove the problem ...[/QUOTE]
I don't have a dog in this game. To be clear.

But a simple question arises - can these three k values be [URL="https://en.wikipedia.org/wiki/Riesel_number"]Riesel numbers[/URL]?
[I]They cannot.[/I]
Then why is it relevant how big the witness primes are?
Does this conjecture need [B]two [/B]witness primes - i.e. these known ones, and the slightly smaller ones?
[I]It does not.[/I]
Am I missing something?

 mathwiz 2021-05-27 23:38

[QUOTE=kar_bon;579200]Before this is cleared, the Riesel problem still stay at 47 open k-values left to prove the problem and I think neither Wilfrid Keller nor any serious prime hunter will rest until this inconsistency is resolved.[/QUOTE]

These are both your opinions, and the former is clearly false.

 Happy5214 2021-05-29 01:25

[QUOTE=kar_bon;579200]Before this is cleared, the Riesel problem still stay at 47 open k-values left to prove the problem and I think neither Wilfrid Keller nor any serious prime hunter will rest until this inconsistency is resolved.[/QUOTE]

The Riesel problem, by definition, is proving whether 509,203 is the smallest Riesel number. These 3 [I]k[/I]'s, with prime [I]n[/I]'s now known, are no longer relevant for that problem. They cannot be the smallest Riesel number. While it would be useful to know the smallest primes for each [I]k[/I], this is not directly related to the Riesel problem as defined. There are 44 [I]k[/I]'s left in the Riesel problem, corresponding to the 44 Riesel [I]k[/I]'s less than 509,203 with no primes known.

 kar_bon 2021-05-29 08:12

I've updated the [url='https://www.rieselprime.de/ziki/Riesel_problem']Wiki page[/url] with those not-PG-found-primes, unreserved them, so no longer listed in their [url='https://www.rieselprime.de/ziki/PrimeGrid_Riesel_Problem']project page[/url], but still left a note for those 3 k-values.
Sure the Riesel problem is to find any n-value of any of the remianing k-values to prove the conjecture.
But from beginning the project every real primesearcher like Keller or Gallot were anxious to know the lowest n-value.
This also prevents to fill in the missing value for k=2293 in this [url='http://oeis.org/A108129']OEIS sequence[/url], because this lists only the lowest n.
Because I could not determine the date when PG stopped the search for those values, I took the 2021-05-01 and the max-n value of the search from their status page.

 mathwiz 2021-05-29 16:51

[QUOTE=kar_bon;579376]Sure the Riesel problem is to find any n-value of any of the remianing k-values to prove the conjecture.
But from beginning the project every real primesearcher like Keller or Gallot were anxious to know the lowest n-value.[/QUOTE]

It does not help your arguments to claim that you are a "real" primesearcher (sp) and others are not, whatever that means.

 kar_bon 2021-05-30 11:07

I've not claimed me a real primesearcher, but thank you for the title.
I'm collecting data in prime numbers for k*2^n-1 (mostly and others, too) for 14 years now (my first page for RPS was in 2007), because there was no data collection in an oversesable form:
many small personal projects, some others only testing some ranges, and all data spread around the net.
You even don't know how much work I've done over the years and how disappointing it is to see only a prime and no further information like tested ranges.
So even if somebody is logged in here, why no further information should be given?
In the primesearch community nothing is more annoying to test open ranges to fill some missing data.
That's my real concern: to document the whole data to avoid duplicate and disappointing work for others.

 matzetoni 2021-05-30 18:17

Just wanted to let you know that your efforts are greatly appreciated, kar_bon!

 paulunderwood 2021-08-08 00:37

Makoto Morimoto has set a new record for a [URL="https://primes.utm.edu/top20/page.php?id=53"]palindrome prime[/URL] at [URL="https://primes.utm.edu/primes/page.php?id=132591"]490001 digits[/URL], :smile:

 LaurV 2021-08-08 08:48

Aren't mersenne prime palindromes themselves? :razz:

 paulunderwood 2021-08-08 09:04

[QUOTE=LaurV;585155]Aren't mersenne prime palindromes themselves? :razz:[/QUOTE]

I base 2 they are. In fact any n>1 is a palindrome in base n+1 and in base n-1 :grin:

 sweety439 2021-08-08 14:07

[QUOTE=LaurV;585155]Aren't mersenne prime palindromes themselves? :razz:[/QUOTE]

All primes p not in [URL="https://oeis.org/A016038"]https://oeis.org/A016038[/URL] are palindromes in some base < p-1

 paulunderwood 2021-09-11 08:21

Congrats to Serge and Ryan for the two smallest known Mega primes, prove with CHG at 28.7% factored of N+1

[URL="https://primes.utm.edu/primes/page.php?id=132705"]10^999999 - 1022306*10^287000 - 1[/URL]

[URL="https://primes.utm.edu/primes/page.php?id=132704"]10^999999 - 1087604*10^287000 - 1[/URL]

:banana: :banana:

 Batalov 2021-09-11 10:44

[QUOTE=paulunderwood;587681]Congrats to Serge and Ryan for the two smallest known Mega primes, prove with CHG at 28.7% factored of N+1
[/QUOTE]
Two [I]largest [/I]known [I]less-than-Mega primes[/I], actually.
(The second one was found before search was called off, an incidental finding. :rolleyes: )

[CODE]...
10^999999+308267*10^292000+1 P 1000000 Batalov 02/2021
10^999999+593499 PRP 1000000 Peter Kaiser 02/2013
10^999999 C 1000000 --- a composite, smallest million-digit number
10^999999-172473 PRP 999999 Patrick De Geest 12/2016
10^999999-1022306*10^287000-1 P 999999 Propper,Batalov 09/2021
10^999999-1087604*10^287000-1 P 999999 Propper,Batalov 09/2021
...[/CODE]

 rudy235 2021-09-11 16:50

[QUOTE=LaurV;585155]Aren't mersenne prime palindromes themselves? :razz:[/QUOTE]

Of course all repunits are “palindromes” per se, but in practical terms when a prime is a Mersenne, a Generalized Mersenne ( to other bases ), repunits, generalized repunits, they are not counted as palindromes in the database of “The primePages”

 paulunderwood 2021-09-12 17:20

Congrats to Marc Wiseler and PrimeGrid for the "321" prime [URL="https://primes.utm.edu/primes/page.php?id=132678"]3*2^17748034-1[/URL] (5,342,692 decimal digits) ranked as the 18th largest known prime.

:banana: :banana: :banana:

 diep 2021-09-12 17:22

[QUOTE=paulunderwood;587767]Congrats to Marc Wiseler and PrimeGrid for the "321" prime [URL="https://primes.utm.edu/primes/page.php?id=132678"]3*2^17748034-1[/URL] (5,342,692 decimal digits) ranked as the 18th largest known prime.

:banana: :banana: :banana:[/QUOTE]

Big congrats!!!!!

 Batalov 2021-09-14 20:08

Another Riesel "other" number is [I]coming soon[/I].

It is a palindrome, chock full of "9"s (with a few others) and is neatly 1,234,567 decimal digits long

 paulunderwood 2021-09-14 21:01

[QUOTE=Batalov;587870]Another Riesel "other" number is [I]coming soon[/I].

It is a palindrome, chock full of "9"s (with a few others) and is neatly 1,234,567 decimal digits long[/QUOTE]

I am looking forward to its revelation. The largest palindrome before this one had 490,001 digits. So 1,234,567 digits is quite amazing considering its crunching is done with generic modular reduction.

 sweety439 2021-09-15 07:15

[QUOTE=paulunderwood;587879]I am looking forward to its revelation. The largest palindrome before this one had 490,001 digits. So 1,234,567 digits is quite amazing considering its crunching is done with generic modular reduction.[/QUOTE]

[URL="https://primes.utm.edu/primes/status.php"]https://primes.utm.edu/primes/status.php[/URL]

id 132704 and 132705 are palindromes.

 paulunderwood 2021-09-15 11:19

[QUOTE=sweety439;587899][URL="https://primes.utm.edu/primes/status.php"]https://primes.utm.edu/primes/status.php[/URL]

id 132704 and 132705 are palindromes.[/QUOTE]

No they are not :no: Reversing the digits does not give the same number.

[url]https://primes.utm.edu/primes/page.php?id=132715[/url] is a palindrome. Congrats Serge and Ryan.

UTM's Prime Pages parser calculated the decimal digits as 1234568 :ermm:

 Batalov 2021-09-15 16:06

[QUOTE=paulunderwood;587905]UTM's Prime Pages parser calculated the decimal digits as 1234568 :ermm:[/QUOTE]
Prof.Caldwell's calculator had insufficient precision. I'll drop him a note. It is, of course, 1234567.

All palindromes of even length (except 11) are composite! :rolleyes:
[SPOILER]Hint: they are divisible by 11[/SPOILER]

 rudy235 2021-09-15 18:17

[QUOTE=paulunderwood;587879]I am looking forward to its revelation. The largest palindrome before this one had 490,001 digits. So 1,234,567 digits is quite amazing considering its crunching is done with generic modular reduction.[/QUOTE]

Wow! A megaprime palindrome. And one with more than twice the digits than the previous one!

I have to see it to believe it!:philmoore:

 Batalov 2021-09-15 21:52

When I was already way into sieving, I thought that I should have picked [C]1234321[/C] decimal digits length :rolleyes:

But it turned out good. With 1234567 digits' dataset the hit came, statistically speaking, [SPOILER]very![/SPOILER] early. So it [URL="https://primes.utm.edu/primes/page.php?id=132715"]was lucky[/URL].

 paulunderwood 2021-09-21 00:39

The prof has been busy. He fixed the palindrome length and puzzle-peter's arithmetic progression, which comes second on table two of [url]https://primes.utm.edu/top20/page.php?id=14[/url].

Hint: An AP9 could be quite easy to find to make it to the top of table two. For the AP8, I wrote my own GWNUM code which was 15% faster, I think mainly by dropping repetitive evaluations of the primorial coefficient. I'd willing to share it with any interested parties.

 Batalov 2021-09-21 01:30

Good! Excellent!
Even Kamada-san wrote to him and cc:'d me (as if I could help :rolleyes: ).

But it is fixed now, cool beans.

 pepi37 2021-09-22 10:07

[QUOTE=Batalov;587937]When I was already way into sieving, I thought that I should have picked [C]1234321[/C] decimal digits length :rolleyes:

But it turned out good. With 1234567 digits' dataset the hit came, statistically speaking, [SPOILER]very![/SPOILER] early. So it [URL="https://primes.utm.edu/primes/page.php?id=132715"]was lucky[/URL].[/QUOTE]

So if it is not secret how many candidates was tested before prime appear?

 ryanp 2021-09-22 12:51

[QUOTE=pepi37;588390]So if it is not secret how many candidates was tested before prime appear?[/QUOTE]

About 18,000 of the ~316K inputs that Serge originally sent me.

P.S. (S.B.) - the exact row number for the hit was 13,239th

 pepi37 2021-09-22 20:54

[QUOTE=ryanp;588395]About 18,000 of the ~316K inputs that Serge originally sent me.

P.S. (S.B.) - the exact row number for the hit was 13,239th[/QUOTE]

13239-th: small number of candidates for such prime. Very lucky hit :)

 rudy235 2021-09-25 01:14

This is an incredible result! [url]https://primes.utm.edu/primes/page.php?id=132738[/url]

But now we have [B][SIZE="4"]two[/SIZE][/B] different record arithmetic progression of 3 elements of 884,748 and 807,954 digits. the other one being. [URL="https://primes.utm.edu/primes/page.php?id=132738"]https://primes.utm.edu/primes/page.php?id=132738[/URL]

Still these AP-3 is truly impressive as the number of digits either is over 70% more than the previous one which was 406,437 digits.

Congratulations to Ryan and Serge.:bounce wave:

 paulunderwood 2021-09-27 20:59

Congrats to James Winskill for the mega primorial prime: [URL="https://primes.utm.edu/primes/page.php?id=132758"]3267113# - 1[/URL] (1,418,398 decimal digits).

:banana:

 rudy235 2021-09-28 00:25

[QUOTE=paulunderwood;588860]Congrats to James Winskill for the mega primorial prime: [URL="https://primes.utm.edu/primes/page.php?id=132758"]3267113# - 1[/URL] (1,418,398 decimal digits).

:banana:[/QUOTE]

Yes, in the last few days we have had two new categories of primes entering the megaprime territory. A [URL="https://en.wikipedia.org/wiki/Palindromic_prime"]Palindromic[/URL] with 1,234,567 digits and this [URL="https://en.wikipedia.org/wiki/Primorial_prime"]Primorial[/URL] with 1,418,398 digits. The next one coming is probably the 3[SUP]rd[/SUP] term of a [URL="https://en.wikipedia.org/wiki/Primes_in_arithmetic_progression"]Prime in A.P.
[/URL]
We now have close to 1,125 megaprimes

 Batalov 2021-09-28 21:57

[QUOTE=rudy235;588876]...A [URL="https://en.wikipedia.org/wiki/Palindromic_prime"]Palindromic[/URL] with 1,234,567 digits and ...[/QUOTE]How about [I]two [/I]of them? :rolleyes:

 paulunderwood 2021-09-29 14:25

[QUOTE=Batalov;588934]How about [I]two [/I]of them? :rolleyes:[/QUOTE]

You mean "two more"?

[url]https://primes.utm.edu/primes/page.php?id=132766[/url]
[url]https://primes.utm.edu/primes/page.php?id=132767[/url]

:banana: :banana:

 rudy235 2021-10-16 17:50

How difficult is to prove a primorial Prime?

[URL="https://primes.utm.edu/primes/page.php?id=132758"]3267113# - 1 [/URL]

[B][COLOR="Navy"]Verification status (*): InProcess[/COLOR][/B]

Is still unproven. I would think that having the primorial +1 100% factored would make proving it a matter of a couple of says. A week in the worse case.

 paulunderwood 2021-10-16 17:54

[QUOTE=rudy235;590778]How difficult is to prove a primorial Prime?

[URL="https://primes.utm.edu/primes/page.php?id=132758"]3267113# - 1 [/URL]

[B][COLOR="Navy"]Verification status (*): InProcess[/COLOR][/B]

Is still unproven. I would think that having the primorial +1 100% factored would make proving it a matter of a couple of says. A week in the worse case.[/QUOTE]

Some numbers require proof attempts at increasing sizes of FFT.

 paulunderwood 2021-10-18 22:55

Two birds with one stone

Congrats tp Ryan and Serge for the record Near-rep Digit / Palindrome prime [URL="https://primes.utm.edu/primes/page.php?id=132851"]10^1888529 - 10^944264 - 1[/URL]

 Batalov 2021-10-18 23:44

[QUOTE=paulunderwood;591030]Congrats tp Ryan and Serge for the record Near-rep Digit / Palindrome prime [URL="https://primes.utm.edu/primes/page.php?id=132851"]10[SUP]1888529[/SUP] - 10[SUP]944264[/SUP] - 1[/URL][/QUOTE]
Yet another custom sieve for such hybrid beasts:
quick sketch:

We are searching for NRP(K,n) = 10[SUP]2n+1[/SUP]-K*10[SUP]n[/SUP]-1. K can only be 1,2,4,5,7,8. (K=3 has algebraic factorization, which is not needed ...because the whole expression is divisible by 3 when 3|K).

Step 1. Let x=10^n, then NRP(K,n) = 10x[SUP]2[/SUP]-Kx-1 . I solve this quadratic equation just like in school but x is some Mod(x,p) then sieve by p

Step 2. If quadratic equation has solution (nearly half the time; if it doesn't , nothing to sieve out), then --

Step 3. Solve 10^n = x[SUB]1[/SUB] and 10^n = x[SUB]2[/SUB]. This is called znlog() and these values will periodically repeat with period znorder().

Step 4. Sieve out and repeat for 7<= p <= 10^11 or 10^12.

Step 5: remove special cases for p={7,11,13} (this actually removes a huge fraction of candidates with K=2, that's why [URL="https://stdkmd.net/nrr/9/99799.htm"]it is the "thinnest" K[/URL])

The trick is to code steps 1, 2 and 3, and to know how.

Step 6. Test. (we test all six number forms in order of size. The fact that K=1 produced the first hit is accidental. With K=1, the number looks a bit more elegant.)

 rudy235 2021-10-19 01:14

[QUOTE=rudy235;590778]How difficult is to prove a primorial Prime?

[URL="https://primes.utm.edu/primes/page.php?id=132758"]3267113# - 1 [/URL]

[B][COLOR="Navy"]Verification status (*): InProcess[/COLOR][/B]

Is still unproven. I would think that having the primorial +1 100% factored would make proving it a matter of a couple of days. A week in the worse case.[/QUOTE]

After 20 days (10/17/21) it was proven prime.

 sweety439 2021-10-20 08:42

[QUOTE=Batalov;591031]Step 5: remove special cases for p={7,11,13} (this actually removes a huge fraction of candidates with K=2, that's why [URL="https://stdkmd.net/nrr/9/99799.htm"]it is the "thinnest" K[/URL])[/QUOTE]

You mean that the [URL="https://www.rieselprime.de/ziki/Nash_weight"]Nash weight[/URL] (or [URL="https://stdkmd.net/nrr/prime/primedifficulty.txt"]difficulty[/URL]) for K=2 (999...9997999...999) is very low?

 Batalov 2021-10-22 04:59

[QUOTE=sweety439;591120]You mean that the [URL="https://www.rieselprime.de/ziki/Nash_weight"]Nash weight[/URL] ...[/QUOTE]
Dare you to define it (for these six sequences), but yes.
[QUOTE=sweety439;591120]... (or [URL="https://stdkmd.net/nrr/prime/primedifficulty.txt"]difficulty[/URL]) for K=2 (999...9997999...999) is very low?[/QUOTE]
Dare you to define it (for these six sequences), but yes.

 pepi37 2021-10-22 08:20

If I may ask how many candidates remain after that ?

 Batalov 2021-10-22 15:57

2 Attachment(s)
[QUOTE=pepi37;591322]If I may ask how many candidates remain after that ?[/QUOTE]
Sure.

 bur 2021-10-22 17:44

New Primorial Prime found

Recently a new -1 type primorial prime was found at PRPNet.

[URL="https://primes.utm.edu/primes/page.php?id=132758"]3267113# - 1[/URL]

It has 1418398 digits, making it the largest known one. The last -1 primorial prime was found more than 9 years ago, so this is quite the finding. The last +1 primorial prime hit is from 2001 btw. 20 years ago. :D

I think it's an interesting type of prime due to its involvement in Euclid's proof of the infinitude of primes. Not many people seem to hunt for them though and they seem somewhat scarce taking into account that N+-1 has lots of factors.

[color=red][B]MODERATOR NOTE:[/b] Moved to this thread, which already has [url=https://www.mersenneforum.org/showpost.php?p=588860&postcount=275]this post[/url] and several followups related to this number.[/color]

 paulunderwood 2021-10-22 18:03

[QUOTE=bur;591379]Recently a new -1 type primorial prime was found at PRPNet.

[URL="https://primes.utm.edu/primes/page.php?id=132758"]3267113# - 1[/URL]

It has 1418398 digits, making it the largest known one. The last -1 primorial prime was found more than 9 years ago, so this is quite the finding. The last +1 primorial prime hit is from 2001 btw. 20 years ago. :D

I think it's an interesting type of prime due to its involvement in Euclid's proof of the infinitude of primes. Not many people seem to hunt for them though and they seem somewhat scarce taking into account that N+-1 has lots of factors.[/QUOTE]

PRP tests for these are quite quick, compared to proofs. However they need generic modular reduction for Fermat PRP tests, whereas small-k Riesel and Proth prime run 4x (?) faster using a special mod.

The rarity of these numbers might put the next beyond the powers of Batalov-Propper.

[color=red][B]MODERATOR NOTE:[/b] Moved to this thread, which already has [url=https://www.mersenneforum.org/showpost.php?p=588860&postcount=275]this post[/url] and several followups related to this number.[/color]

 bur 2021-10-25 17:34

Thanks for moving the post.
[QUOTE]The rarity of these numbers might put the next beyond the powers of Batalov-Propper.[/QUOTE]Who knows, it's not like where GIMPS is currently at where 20M+ consecutive candidates are composite - at least I don't think so.

I always forget the estimate for the digit size of primorials but the FFT size remains very managable even up to 20,000,000# where it's 3M.

So if anyone was willing to put some larger ressources towards primorials or factorials, I'm pretty sure it'll yield some nice results before ending up in GIMPS waters.

 Dr Sardonicus 2021-10-25 20:53

[QUOTE=bur;591586]I always forget the estimate for the digit size of primorials but the FFT size remains very managable even up to 20,000,000# where it's 3M.[/QUOTE]The number of decimal digits in p[sub]k[/sub] is roughly p[sub]k[/sub]/ln(10). We have

? 3267113/log(10)
%1 = 1418889.1476543787883927627556683863802

As indicated above, 3267113# - 1 actually has 1418398 digits.

The estimate is a consequence of the Prime Number Theorem, which gives the asymptotic estimate

ln(p[sub]k[/sub]#) = ln(2) + ln(3) + ... + ln(p[sub]k[/sub]) ~ p[sub]k[/sub]

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