20100724, 18:18  #1 
May 2010
Prime hunting commission.
2^{4}·3·5·7 Posts 
Thread for posting tiny primes
If you're willing to post some, post away. Please refrain from posting the decimal expansion of the number you're submitting, and please ensure the following:
1. Has no factors below 2^{30} 2. Passes a pseudoprimality test (Recommendation: 13 bases) 3. Is not a "small" prime. (Please ensure it is ≥ 1000 digits.) Submissions by me: 12085 * 2^{6000} + 1 (1811 digits) 895 * 2^{7526} + 1 (2269 digits) 150^{2048} + 1 (4457 digits) 9731 * 1296^{2600} + 1 (8097 digits) 1219 * 2^{6394} + 1 (1928 digits) 1534^{4096} + 1 (13050 digits) 10462 * 1296^{8192} + 1 (25503 digits) 59991 * 2^{91360} + 1 (27507 digits) 2 * 856! + 1 (2140 digits) 2 * 969! + 1 (2475 digits) Expected primes: k * 77096^{8192} + 1 (4007540080 digits) (To be found tonight or tomorrow.) Last fiddled with by 3.14159 on 20100724 at 19:18 
20100724, 19:19  #2 
May 2010
Prime hunting commission.
2^{4}·3·5·7 Posts 
Disregard the last two, they're divisible by 859 and 71833. (Mods, please delete the last two on the list.)
More submissions: 1125 * 2^{6300} + 1 (1900 digits) 39600^{256} + 1 (1178 digits) 2520^{1024} + 1 (3484 digits) 192 * p_{124}# ^{5} + 1 (1436 digits) Still looking for more ProthGFNs. I figured they would be easy to find in the 1015k digit range. Last fiddled with by 3.14159 on 20100724 at 20:05 
20100724, 22:36  #3 
May 2010
Prime hunting commission.
2^{4}×3×5×7 Posts 
A few are probably wellknown cases. (Ex: The generalized Fermat numbers I listed.). Both searches haven't turned up much of anything as of yet (4007540080 digit prime, and a 1464014645 digit prime search. Rather close to 11^{4}.)
Some more submissions: 9787 * 2^{6030} + 1 (1820 digits) 4713 * 2^{4713} + 1 (1423 digits) 1065 * 2^{6303} + 1 (1901 digits) 1881 * 2^{6327} + 1 (1908 digits) Last fiddled with by 3.14159 on 20100724 at 23:04 
20100724, 23:11  #4 
Mar 2006
Germany
43×67 Posts 
Here's a quick shot:
4972*3^16384+1 is prime! (7821 digits) 13506*3^16384+1 is prime! (7822 digits) 43728*3^16384+1 is prime! (7822 digits) 50490*3^16384+1 is prime! (7822 digits) So you want to collect those small primes? You could do a list of the Sierpinski (Proth) side of primes like I do for the Riesel side. I got thousands of them listed! Last fiddled with by kar_bon on 20100724 at 23:26 
20100724, 23:31  #5  
May 2010
Prime hunting commission.
11010010000_{2} Posts 
Quote:
I just have a few searches to finish. (A 40kdigit search, and a 14640digit search.) More submissions: 1036 * 12^{5012} + 1 (5412 digits) 770 * 12^{5002} + 1 (5401 digits) Last fiddled with by 3.14159 on 20100724 at 23:37 

20100724, 23:38  #6  
Mar 2006
Germany
43·67 Posts 
Quote:
I only list base2 primes. Perhaps you can program a converter from k*b^n+1 to k*2^b+1 and I can tell you, if I got the other half of the twin! 

20100724, 23:39  #7  
May 2010
Prime hunting commission.
3220_{8} Posts 
Quote:
I expect the 14640digit search to be finished later today. The search is k * 3754^{4096} + 1 The main search I'm concerned about: k * 77906^{8192} + 1 Last fiddled with by 3.14159 on 20100724 at 23:42 

20100724, 23:43  #8 
Mar 2006
Germany
2881_{10} Posts 

20100724, 23:45  #9  
May 2010
Prime hunting commission.
2^{4}×3×5×7 Posts 
Quote:
Quote:
Last fiddled with by 3.14159 on 20100724 at 23:47 

20100725, 00:08  #10  
Mar 2006
Germany
43·67 Posts 
Quote:
Your original question: No, Riesel numbers are known and the Riesel problem want to find the smallest of them (k=509203 seems the candidate but not proven yet). Riesel primes are so called, because H.Riesel listed k*2^n1 for some small kvalues and small nvalues first (in the 1950's if I'm right). And yes: The difficulty for testing Proth or Riesel primes are the same. Last fiddled with by kar_bon on 20100725 at 00:11 

20100725, 00:15  #11  
May 2010
Prime hunting commission.
690_{16} Posts 
Quote:
Last fiddled with by 3.14159 on 20100725 at 00:17 

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