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Kosmaj 2007-12-26 07:26

[I][The following post is about 281*2^628898-1, a prime found by Cruelty in December 2007.][/I]

Cruelty, a nice and important prime because k=281 was the only k<300 with no primes with more than 100k bits!

Next target: 200k bits, there are 4 Ks with no primes larger than 200k bits: k=109, 221, 233, and 283. All reserved by you !! The one with the minmax prime is k=221: n=104846.

Kosmaj 2007-12-26 07:39

The 4 Ks < 300 with minmax (smallest largest) primes are now:

k=221, n=104846
k=109, n=141227
k=283, n=149351
k=233, n=179992

All tested to 600k, and all currently reserved by Cruelty.

Kosmaj 2008-07-07 00:23

MinMax Status Update
Last time mentioned [URL=""]here[/URL]

The only two k<300 with largest known prime smaller than 200k bits are now:

k=283, n=149351
k=233, n=179992

Both tested to 920k and reserved by Cruelty.

Kosmaj 2010-02-11 04:54

Update on k<300 minmax primes:

k largest prime
233 179992
13 233207
191 240802
249 251036[/CODE]

All are tested up to n=1M or more.
The largest primes of all other Ks have 300k digits or more.

k=283 was removed from the top of the list by Cruelty.
Its largest prime was at n=149351, but now it's at n=1702599.

The previous status can be found [URL=""]here[/URL].

Kosmaj 2012-05-05 06:12

I moved this discussion to a separate thread.

In the meanwhile the following primes were found
233*2^1700734-1 by Cruelty, July 2010
13*2^2606075-1 by Curtis, December 2011
13*2^2642943-1 by Curtis, February 2012

Therefore, there are now only three k<300 which largest known prime has less than 300k binary bits:
k=191 at n=240802, tested up to n=4.2M
k=249 at n=251036, tested up to n=1.1M
k=151 at n=263895, tested up to n=2.9M

All other k<300 have largest known primes with more than 300k bits.

VBCurtis 2012-05-05 16:56

151 263895 is under 300k bits.

I count 7 others below 500k bits:
7 372897
37 341365
43 399767
225 491135
239 356300
275 398928
295 389903

Kosmaj 2012-05-05 22:56

Curtis, thanks for listing other candidates and specially for the correction about k=151, I missed that one. :smile:

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