mersenneforum.org  

Go Back   mersenneforum.org > Prime Search Projects > Riesel Prime Search

Reply
 
Thread Tools
Old 2007-07-27, 17:35   #1
gd_barnes
 
gd_barnes's Avatar
 
May 2007
Kansas; USA

101000000001102 Posts
Default k's with consecutive small primes

I did some testing on k's with consecutive small primes, i.e. k's that have primes from n=1 thru 6, 1 thru 7, 1-8, etc. up to k=100M. Some of the k's that I found may be excellent candidates for people to search further so I'm listing them here. The ones that are prime for n=1 thru 7 and higher are listed below and I'm attaching a list of the k's that are prime for n=1 thru 6.

Up to k=100M, the following k's are prime for:

n=1 thru 9
42932385

n=1 thru 8
26277285

n=1 thru 7
1082115
1164735
5128905
5154945
7015155
12088065
14421825
18544365
31400085
44087025
47915595
52694085
60627945
69070365
91780965
94708605
95082405

The biggest surprise out of all of this that I found was that k=45 is the only k < 26K that is prime for n=1-5 and is the only k < 200K that is prime for n=1-6!! :surprised

If anyone knows the lowest k that is prime for n=1-10 or would like to do some testing to find it, I'd be interested in seeing the results. I think you'd probably have to test up to k=1G. I was lucky to find one that was prime for n=1-9 out of only 2 candidates that were prime for n=1-8.


Gary
Attached Files
File Type: txt cons-small-prime-1-6.txt (1.4 KB, 150 views)
gd_barnes is offline   Reply With Quote
Old 2007-07-30, 23:26   #2
gd_barnes
 
gd_barnes's Avatar
 
May 2007
Kansas; USA

280616 Posts
Default No k's with primes n=1 to 10 up to k=10G

An update here...

I extended this search by 100X all the way up to k=10G. There were still no k's that were prime for n=1 thru 10! One big thing that makes 10 consecutive primes harder is the factor of 11. If the k is not divisible by 11 and there's not a 'covering set' of other factors to eliminate it, it occurs (at least) once every 10 n. Over 1/3rd of the k's that were prime for n=2 thru 10 had a factor of 11 for n=1. Obviously the same situation would occur at any number of consecutive primes that is a low prime number minus 1.

I did find one that has 10 consecutive primes though. k=6522452145 is prime for n=2 thru 11. That's a more rare find than one that is prime for n=1 thru 10, so that's a good thing.


Gary
gd_barnes is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Prime Gap Length with consecutive integers divisible by small primes carpetpool Prime Gap Searches 45 2017-09-30 20:51
Largest Known Pair of Consecutive Primes a1call Information & Answers 8 2017-02-06 17:30
Unexpected biases in the distribution of consecutive primes axn Lounge 21 2016-06-05 13:00
Sieving with powers of small primes in the Small Prime variation of the Quadratic Sieve mickfrancis Factoring 2 2016-05-06 08:13
Small primes kar_bon Riesel Prime Data Collecting (k*2^n-1) 3 2013-05-11 04:56

All times are UTC. The time now is 03:56.

Wed Dec 2 03:56:16 UTC 2020 up 83 days, 1:07, 1 user, load averages: 2.45, 2.13, 1.84

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.