20071226, 07:26  #1 
Nov 2003
111000100110_{2} Posts 
[The following post is about 281*2^6288981, a prime found by Cruelty in December 2007.]
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. Last fiddled with by Kosmaj on 20120505 at 06:16 
20071226, 07:39  #2 
Nov 2003
2×1,811 Posts 
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. 
20100211, 04:54  #4 
Nov 2003
2×1,811 Posts 
Update on k<300 minmax primes:
Code:
k largest prime 233 179992 13 233207 191 240802 249 251036 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 here. 
20120505, 06:12  #5 
Nov 2003
3622_{10} Posts 
I moved this discussion to a separate thread.
In the meanwhile the following primes were found 233*2^17007341 by Cruelty, July 2010 13*2^26060751 by Curtis, December 2011 13*2^26429431 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. Last fiddled with by Kosmaj on 20120505 at 22:57 
20120505, 16:56  #6 
"Curtis"
Feb 2005
Riverside, CA
2^{2}·7·13^{2} Posts 
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 Curtis 
20120505, 22:56  #7 
Nov 2003
3622_{10} Posts 
Curtis, thanks for listing other candidates and specially for the correction about k=151, I missed that one.

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