RPS k<300 minmax status

Kosmaj · 2007-12-26, 07:26

[The following post is about 281*2^628898-1, 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.

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

Last time mentioned here

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:

Code:

 k   largest prime
233	179992
 13     233207
191	240802
249	251036

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 here.

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
-Curtis

Kosmaj · 2012-05-05, 22:56

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

2007-12-26, 07:26	#1
Kosmaj Nov 2003 2·1,811 Posts	[The following post is about 2812^628898-1, 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 2012-05-05 at 06:16

2008-07-07, 00:23	#3
Kosmaj Nov 2003 2×1,811 Posts	MinMax Status Update Last time mentioned here 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.

2010-02-11, 04:54	#4
Kosmaj Nov 2003 2×1,811 Posts	Update on k<300 minmax primes: Code: k largest prime 233 179992 13 233207 191 240802 249 251036 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 here.

2012-05-05, 06:12	#5
Kosmaj Nov 2003 2·1,811 Posts	I moved this discussion to a separate thread. In the meanwhile the following primes were found 2332^1700734-1 by Cruelty, July 2010 132^2606075-1 by Curtis, December 2011 132^2642943-1 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. Last fiddled with by Kosmaj on 2012-05-05 at 22:57*

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2007-12-26, 07:39	#2
Kosmaj Nov 2003 111000100110₂ 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.

2012-05-05, 16:56	#6
VBCurtis "Curtis" Feb 2005 Riverside, CA 12244₈ 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

2012-05-05, 22:56	#7
Kosmaj Nov 2003 2·1,811 Posts	Curtis, thanks for listing other candidates and specially for the correction about k=151, I missed that one.