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]

[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.

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.

[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?

[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.

[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.

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.

[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.

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.

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

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: