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-   Sierpinski/Riesel Base 5 (https://www.mersenneforum.org/forumdisplay.php?f=54)

 Joe O 2010-05-26 02:09

Project Description

1 Attachment(s)
This project is an extension of the original Sierpinski/Riesel problems. It is attempting to solve the Sierpinski/Riesel problems for base 5 by determining the smallest Sierpinski/Riesel base 5 numbers. Therefore, primes of the form k*5^n+/-1 are being sought for even k's.

A distributed effort is currently ongoing in support of the project.

[B][U]Sierpinski Base 5[/U][/B] - The smallest even k Sierpinski base 5 number is suggested to be k=159986. To prove this, it is sufficient to show that k*5^n+1 is prime for each even k < 159986. This has currently been achieved for all even k, with the exception of the following 47 values:
[B]k = [/B][U]6436, 7528, 10918, 24032, 26798, 29914, 31712, 36412, 37292, 41738, 44348, 44738, 45748, 51208, 55154, 58642, 59912, 60394, 62698, 64258, 67612, 67748, 68492, 71492, 74632, 76724, 77072, 81556, 83936, 84284, 90056, 92158, 92182, 92906, 93484, 105464, 109208, 109988, 110488, 118568, 126134, 133778, 138514, 139196, 144052, 152588, 154222
[/U]
[B][U]Riesel Base 5[/U][/B] - The smallest even k Riesel base 5 number is suggested to be k=346802. To prove this, it is sufficient to show that k*5^n-1 is prime for each even k < 346802. This has currently been achieved for all even k, with the exception of the following 130 values
[B]k = [/B][U]1396, 2488, 3622, 4906, 5374, 11812, 17152, 18656, 22478, 22934, 23906, 26222, 27994, 35248, 35816, 48764, 49568, 52922, 53546, 57406, 63838, 64598, 66916, 68132, 70082, 71146, 72532, 76354, 81134, 84466, 88444, 92936, 97366, 97768, 100186, 102818, 102952, 102976, 104944, 109238, 109838, 109862, 114986, 119878, 127174, 130484, 131848, 134266, 136804, 138172, 143632, 145462, 145484, 146264, 146756, 147844, 150344, 151042, 152428, 154844, 159388, 162434, 162668, 164852, 170386, 170908, 171362, 173198, 174344, 175124, 177742, 178658, 180062, 182398, 187916, 189766, 190334, 194368, 195872, 201778, 204394, 206894, 207394, 207494, 210092, 213988, 231674, 238694, 239062, 239342, 243686, 243944, 245114, 246238, 248546, 256612, 259072, 262172, 265702, 266206, 267298, 268514, 270748, 271162, 273662, 285598, 285728, 289184, 296024, 298442, 301016, 301562, 304004, 305716, 306398, 313126, 316594, 318278, 322498, 325918, 325922, 326834, 327926, 329584, 330286, 331882, 335414, 338866, 338948, 340168[/U]

[B][U]History[/U][/B]
Robert Smith originally presented the idea of a Sierpinski/Riesel base 5 search on [URL="http://tech.groups.yahoo.com/group/primeform/message/4739"]2004-9-17[/URL], in the primeform yahoo group. Using {3,7,13,31,601} as the covering set, he proposed that k=346802 is the smallest Riesel base 5 number. Shortly afterwards, Guido Smetrijns proposed that k=159986 is the smallest Sierpinski base 5 number.
After doing most of the initial work himself, Robert posted in the mersenneforum.org on [URL="http://www.mersenneforum.org/showthread.php?t=3125"]2004-9-28[/URL], and thus, the distributed effort began. Other principle players in the development, management, and growth of the project are Lars Dausch, Geoff Reynolds, Anand S Nair, and Thomas Masser.

[B][U]Primes Reported[/U][/B]
As of 2011-01-02 there have been 352 primes reported in this forum, 1 of them this year: [URL="http://www.mersenneforum.org/showthread.php?t=14510"]S/R Base 5 Primes in 2011 [/URL]

There were 33 primes reported in 2010. [URL="http://www.mersenneforum.org/showthread.php?t=13861"]S/R Base 5 Primes in 2010 [/URL]
There were no primes reported in 2009.
There were 10 primes reported in 2008.
There were 31 primes reported in 2007.
There were 126 primes reported in 2006.
There were 129 primes reported in 2005.
There were 22 primes reported in 2004, the starting year of this project.

 Aillas 2012-05-11 14:45

Not up to date. If you have time:

It seems it's now 45 SB5 & 117 RB5.
Stat for 2011 too?

Thanks.

 Joe O 2016-03-11 21:49

[QUOTE=Aillas;299168]
Stat for 2011 too?

Thanks.[/QUOTE]

[url="http://www.mersenneforum.org/showthread.php?t=14510"]S/R Base 5 Primes in 2011[/url]

[url="http://www.mersenneforum.org/showthread.php?t=16509"]S/R Base 5 Primes in 2012[/url]

2013 see post just above this one

[url="http://www.mersenneforum.org/showthread.php?t=20637"]S/R Base 5 Primes in 2014[/url]

[url="http://www.mersenneforum.org/showthread.php?t=20639"]S/R Base 5 Primes in 2015[/url]

[url="http://www.mersenneforum.org/showthread.php?t=20847"]S/R Base 5 Primes in 2016[/url]

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