[QUOTE=sweety439;473027]Reserve 513<=b<=1024, also for 1 <= n <= 1024.[/QUOTE]

Release this reservation to reserve the generalized repunit primes in negative bases -414, -416, -428, -433, -434 and -445.

[QUOTE=sweety439;473088]Release this reservation to reserve the generalized repunit primes in negative bases -414, -416, -428, -433, -434 and -445.[/QUOTE]

Continue for this reservation...

[QUOTE=sweety439;474030]Continue for this reservation...[/QUOTE]

Update the status file for bases 513 to 1024. (also searched to n=1024)

[QUOTE=sweety439;474228]Update the status file for bases 513 to 1024. (also searched to n=1024)[/QUOTE]

For the file:

1st: (b-1)*b^n-1
2nd: (b-1)*b^n+1
3rd: (b+1)*b^n-1
4th: (b+1)*b^n+1
1st dual: b^n-(b-1)
2nd dual: b^n+(b-1)
3rd dual: b^n-(b+1)
4th dual: b^n+(b+1)

Range: 1<=n<=1024 (since we do not include n=0, but include n=1)

Update the file for bases 2<=b<=1024. (the range of n is also 1<=n<=1024)

202*201^31274+1 (72033 digits) is prime.

[QUOTE=kar_bon;477248]202*201^31274+1 (72033 digits) is prime.[/QUOTE]

Thanks for the smallest Williams primes of 4th kind base 201!!!

The first few forms with no known (probable) primes are:

93, 1st dual (93^n-92)
113, 1st dual (113^n-112)
113, 2nd dual (113^n+112)
123, 2nd (122*123^n+1)
123, 2nd dual (123^n+122)
128, 1st (127*128^n-1)
152, 1st dual (152^n-151)
158, 1st dual (158^n-157)
173, 2nd dual (173^n+172)
179, 2nd dual (179^n+178)
188, 1st dual (188^n-187)

You can also reserve them.

For the 1st dual form of base 293 (293^n-(293-1)), I searched up to n = 10k and found the following PRP's:
[CODE]293^3205-292
293^5489-292
293^7781-292[/CODE]

If you found a prime of the form (b+-1)*b^n+-1 or b^n+-(b+-1), you can post it in this. (I did not double-check it, so it may have errors)

"... not double-check... may have errors..."

What are you doing here?

Uploading a new file for Williams primes without checking them for errors or even update it?

1. The found primes from post #61 and #63 are not given.
2. The primes in post #52 are not given. Where are they from?
3. There're no search ranges you've done in the text-file or any date given of the last update. You should do this because no one will never find any hint for this anymore if the file was downloaded.
4. Specify references for the data you show. A link to the forum thread in that file will help also.
5. Some explanations what these numbers are for would help most: the title is not the only way.

Finally: Only giving hundreds of numbers in a file will help none to search seriuosly. Show some scientific methods and backgrounds so others could/will join your search.

[QUOTE=kar_bon;477654]"... not double-check... may have errors..."

What are you doing here?

Uploading a new file for Williams primes without checking them for errors or even update it?

1. The found primes from post #61 and #63 are not given.
2. The primes in post #52 are not given. Where are they from?
3. There're no search ranges you've done in the text-file or any date given of the last update. You should do this because no one will never find any hint for this anymore if the file was downloaded.
4. Specify references for the data you show. A link to the forum thread in that file will help also.
5. Some explanations what these numbers are for would help most: the title is not the only way.

Finally: Only giving hundreds of numbers in a file will help none to search seriuosly. Show some scientific methods and backgrounds so others could/will join your search.[/QUOTE]

I have searched all kinds of both (original and dual) forms of all bases 2<=b<=1024 up to n=1024, there are no errors in the file in the post [URL="http://mersenneforum.org/showpost.php?p=474228&postcount=58"]#58[/URL].

Thus, you can search n>1024 for a single kind of a single base.