There are 3 bases and one prime omitted on the primes page per statuses shown in this post:
[URL]http://mersenneforum.org/showpost.php?p=435251&postcount=70[/URL]

Base 1656 complete to n=70K.
no primes

Base 2482 complete to n=18735.
prime: (2482^18735+1)^2-2

Base 2634 complete to n=66K.
no primes

Note that ongoing statuses were provided by Sergey in several posts as the bases progressed as he attempted to find primes for all bases <= 3000. It is a good assumption that the bases were entirely searched to their depth shown in the above post.

A doublecheck is complete to n=2500 on all 3 of these bases per my previous post. No primes were found.

Gary, thanks for the updates/corrections. I have applied all of them and updated the webpage. I don't know if I mistyped the numbers or if they were wrong on the page that I imported them from. Had I retested all of those bases myself, I would likely written a program to generate the starting html based upon an input list of primes.

There is also an error for b=640.

[QUOTE=Batalov;477535]There is also an error for b=640.[/QUOTE]

Which is?

I will doublecheck your corrections shortly. :smile:

I am also in the process of verifying the primality of all shown primes for n>2500. This is not an actual doublecheck so there could be missing primes that we are not aware of and any composites that I find could be a simple typo for a different prime and there would be no way for us to know.

What I will do if I find a composite is check the various statuses for the base and see if it is just a simple typo that can be corrected.

Some of the primes are quite large so this will take a day or a little more on one slow core. I started early this morning.

In doing this I happened to visually observe a couple of things that looked strange that you can could quickly correct. One of them happened to be Sergey's find. The base 640 prime that you show is far larger than any other search depth that he did so it looked out of place. Here are those errors:

composites to remove:
(170^9373+1)^2-2 has factor 7
[Note that you listed n=9373 as prime on both sides of base 170. This looked suspect to me so I checked both and found the error.]

incorrect primes to change:
(640^252220+1)^2-2 has factor 23; should be (640^44940+1)^2-2
[Note that you showed the number of digits for n=44940 as the exponent.]
See: [url]http://mersenneforum.org/showpost.php?p=434861&postcount=60[/url]

Please be aware that these were just on a visual inspection. I'm still in the process of checking the primality of all n>2500. I hope do be done late Monday.

I have doublechecked your corrections per my previous posts. The following 4 corrections still need to be made:

There is one base and a prime omitted per statuses shown in this post:
[URL="http://mersenneforum.org/showpost.php?p=435251&postcount=70"]http://mersenneforum.org/showpost.ph...1&postcount=70[/URL]
Base 2482 complete to n=18735.
prime: (2482^18735+1)^2-2
(Note that he had provided previous statuses as this base progressed so it is fair to assume that it was fully completed to n=18735.)

There are also 3 cosmetic errors:

base 2 +1 side; there is a comma but no space between between primes n=17 and n=18;
i.e. 15, 17,18, 21, 23, etc.

base 18 -1 side; there are two commas after prime n=10208;
i.e. 4074, 10208,, 15123, 19395

base 28 +1 side; there is no comma after prime n=5048;
i.e. 586, 993, 5048 24990

Those plus the two corrections for bases 170 and 640 for primes n>2500 shown in my last post.

There're two other errors:

base 54(-1): 8068 instead 8088 (see [url='https://artofproblemsolving.com/community/c390681h1562771']here[/url], I've checked this one)

base 44:
I've done both sides up to n=40k (will continue to 50k).
error: (-1) side: 12909 instead 13909

new one: (44^25786-1)^2-2

I believe that I have made the desired changes and corrections. Please let me know if there are any more.

One more correction: base 290 should be open, as yasyannyasha has released it. See here: [URL="http://www.mersenneforum.org/showpost.php?p=472759&postcount=94http://"]http://www.mersenneforum.org/showpost.php?p=472759&postcount=94[/URL]

I have verified all corrections up through post #136. Everything looks good to that point.

I have completed running a primality test for all primes n>2500 shown on [URL]http://www.mersenneforum.org/rogue/ckps.html[/URL]. I started this prior to post #134 and so "re-confirmed" the corrections pointed out by Karsten and me in the 3 posts after that. 6 additional errors were found (one of them cosmetic) shown below along with some explanations:

[B] composites to remove:[/B]
(26^215057+1)^2-2 has factor 7; No known reporting.

[B] incorrect primes to change:[/B]
(22^72820-1)^2-2 has large factor > 100G; should be (20^72820-1)^2-2; Copied incorrectly from primes post #13.
(22^8642-1)^2-2 has factor 4649; should be (22^8643-1)^2-2; Reported incorrectly on primes post #6.
(40^5369-1)^2-2 has factor 167; should be (40^5639-1)^2-2; No known reporting.
(126^4515+1)^2-2 has factor 250301903; should be (126^4514+1)^2-2; Copied incorrectly from primes post #33.

[B]Cosmetic error:
[/B] (182^310-1)^2-2 has a greater than ">" sign before it;
i.e. >310

With each composite that I found, I was able to come up with the correct prime by either (1) checking various transpositions and single-digit errors in the exponent -or- (2) finding the correct prime in a prior post; with one exception: The huge prime for base 26 shown above. It is very out of place and much larger than anything else in that area. I tried various combinations of removing digits and transpositions with the exponent and had no luck.

Mark, I'll be curious if you know where (26^215057+1)^2-2 came from and if there really is a prime in that area. If it really is that big, it is well into top-5000 range. I could find no top-5000 prime for this form for base 26.

I did a cursory check on the searched to, status date, and reserved by fields on the primes page. It was by no means a comprehensive check. Mark, I am taking the term "status date" literally. In come cases it looks like you have used the column as a last update date. (Perhaps in the future it could be blanked out unless the base is reserved. Kind of a "last status date" for reserved bases only.) Problems:

base 6; change date to 2018/01/10; change to reserved by Dylan14. Reserved to n=150K per reservations post #95.
base 20; change date to 2016/05/05; remove reservation (unless Jiahao He is some secret searcher who does not post here). Per old primes post #13. Inactive for over a year so assumed released.
base 26 change depth to n=84239; change date to 2016/08/27. Per old reservations post #66. Inactive for over a year so assumed released.
base 30; change date to 2016/05/05. Per old primes post #13. Inactive for over a year so assumed released.
base 40; change date to 2016/05/05. Per old primes post #13. Inactive for over a year so assumed released.
base 290; change date to 2017/11/04; remove reservation. Completed to n=20K and released by Dylan14 per reservations post #87. Reserved and then released again with no work done by vasyannyasha on 2017/11/30 per reservations post #94.
base 640; change depth to n=44940; change date to 2016/05/26; Most likely searched until the prime was found in primes post #60 and then released.
base 1656; change date to 2016/06/18. Per edit date in old primes post #70. Inactive for over a year so assumed released.
base 2482; change date to 2016/05/31. Most likely searched until the prime was found in primes post #70 and then released.
base 2634; change date to 2016/06/18. Per edit date in old primes post #70. Inactive for over a year so assumed released.


I'm done checking everything for now although I might do some doublechecking on n=2500-10K sometime in the future. :smile::rolleyes: