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 2007-01-09, 22:22 #1 michaf     Jan 2005 1110111112 Posts Sierpinski / Riesel - Base 22 Sierpinski / Riesel - Base 22 Conjectured Sierpinski at 6694 [5,23,97] Conjectured Riesel at Riesel 4461 [5,23,97] Pesky 17 k's include (now 13 to go) Sierpinski: 22 (cedricvonck) 484 (cedricvonck) 1611 (michaf tested upto 12000) 1908 (michaf tested upto 12000) 4233 (michaf tested upto 12000) 5128 (michaf tested upto 12000) 5659 (michaf tested upto 12000) 6462 (michaf tested upto 12000) Riesel: 1013 (michaf tested upto 12000) 2853 (michaf tested upto 12000) 3104 (michaf tested upto 12000) 3656 (michaf tested upto 12000) 4001 (michaf tested upto 12000) 22 and 484 are special cases; only non-trivials occur with n=2^m If a prime is found for 22 case, 484 is also eliminated (n is one lower in that case) (larger) primes found: 4118*22^12347-1 (michaf) 6234*22^16010+1 (michaf) 942*22^18359+1 (michaf) 5061*22^24048+1 (michaf) 22*22^n+1 / 484*22^n+1 status: Code: below (512): proven composite with phrot (512) 22^512+1 has factor 115443366400367617 (1k) 22^1024+1 has factor 2095383775764481 (2k) 22^2048+1 has factor 65465822271579614082713282973697 (4k) 22^4096+1 has factor 40961 (8k) 22^8192+1 has factor 147457 (16k) 22^16384+1 has factor 2342241402881 (32k) 22^32768+1 has factor 65537 (64k) 22^65536+1 has factor 27918337 (128k) 22^131072+1 has factor 786433 (256k) 22^262144+1 has factor 29884417 (512k) 22^524288+1 has factor 93067411457 (1M) no factors upto 1607651162167705601 (also P-1 stage 1 done with B1=100000 and 25 ECM curves, B1=1000, B2=100000) (2M) no factors upto 285159626880581633 (4M) no factors upto 556968483053633537 (8M) no factors upto 9221584136710389761 (stopping here) (16M) 22^16777216+1 has factor 189162539974657 (32M) 22^33554432+1 has factor 21096518178045953 (64M) no factor upto 9202942106325221377 (stopping here) (128M) 22^134217728+1 has factor 91268055041 (256M) 22^268435456+1 has factor 7368180622415626241 (512M) no factor upto 9187751282130026497 (stopping here) (1G) no factor upto 9159662798383349761 (stopping here) Last fiddled with by michaf on 2007-01-29 at 22:45
2007-01-10, 07:24   #2
ValerieVonck

Mar 2004
Belgium

5×132 Posts
base 22

n = 22 tested to 144895
Attached Files
 lresults22.txt (5.6 KB, 459 views)

2007-01-10, 16:27   #3
fatphil

May 2003

22×61 Posts

Quote:
 Originally Posted by CedricVonck n = 22 tested to 144895
Containing
<<<
22*22^511+1 is not prime.
22*22^2047+1 is not prime.
22*22^3583+1 is not prime.
22*22^6655+1 is not prime.
>>>

Are you sure you know what you're doing?
Those are 22^n+1, which can only ever be prime if n=2^m for some n, namely generalised Fermat numbers.

2007-01-10, 18:55   #4
Xentar

Sep 2006
Germany

2·5·19 Posts

Quote:
 Originally Posted by fatphil Containing <<< 22*22^511+1 is not prime. 22*22^2047+1 is not prime. 22*22^3583+1 is not prime. 22*22^6655+1 is not prime. >>> Are you sure you know what you're doing? Those are 22^n+1, which can only ever be prime if n=2^m for some n, namely generalised Fermat numbers.
eh.. is it the same with
18 * 18^n+1 ?
and if not, could you please try to explain it to me? (Yea, I'm trying to learn the math behind these projects )

2007-01-10, 19:13   #5
fatphil

May 2003

22×61 Posts

Quote:
 Originally Posted by Xentar eh.. is it the same with 18 * 18^n+1 ? and if not, could you please try to explain it to me? (Yea, I'm trying to learn the math behind these projects )
They are also just 18^n+1. Again, they can only be prime if n is a power of 2, and would be Generalised Fermat Numbers. Have a look at Yves Gallot's GFN page for more info.

 2007-01-10, 22:32 #6 michaf     Jan 2005 479 Posts 4118*22^12347-1 is prime 6234*22^16010+1 is prime tests now at 18000
 2007-01-11, 05:43 #7 geoff     Mar 2003 New Zealand 48516 Posts If you want to sieve the GFN's, srsieve should recognise them as such and use a faster method of sieving as long as only the terms of the form n=2^m+1 appear in the input file. If you start srsieve with the -v option it will print a message something like filtering for primes of the form (2^m)x+1' if it has recognised the sequence as GFN. (If there are non-GFN sequences in the sieve as well then it will still notice the GFN's, but most of the benefit will be lost).
2007-01-11, 11:18   #8
ValerieVonck

Mar 2004
Belgium

11010011012 Posts

Quote:
 Originally Posted by fatphil Containing <<< 22*22^511+1 is not prime. 22*22^2047+1 is not prime. 22*22^3583+1 is not prime. 22*22^6655+1 is not prime. >>> Are you sure you know what you're doing? Those are 22^n+1, which can only ever be prime if n=2^m for some n, namely generalised Fermat numbers.
Apperantely not then... Like I said I used NewPGen to sieve the file:
Code:
k*b^n-1 with k fixed
k = 22
b = 22
n from 2 to 1.000.000`
Then I fired up LLR.exe (3.7.1)

 2007-01-12, 19:23 #9 michaf     Jan 2005 1DF16 Posts 942*22^18359+1 is prime 5061*22^24048+1 is prime
 2007-01-13, 03:05 #10 jasong     "Jason Goatcher" Mar 2005 350710 Posts In terms of 22^(2^m)+1, is it possible to figure the odds that at least one value of m will yield a prime for the equation? Since the numbers get big so quickly, I'm thinking it's possible this may be a Sierpinski number that may never be proven, or at least not within my lifetime. Can anybody do the math and figure the chance that it would or wouldn't yield prime if every single m value could be figured at once for the above equation? Last fiddled with by jasong on 2007-01-13 at 03:05
 2007-01-13, 09:32 #11 michaf     Jan 2005 479 Posts The chances are quite slim I suspect, but sieving can be done quite easily. I have started yesterday a sieve for the first 4 numbers left, and that one did 40Mp/sec (now only 3 left since a factor was found for 512k) It will reach the limit of srsieve in about 1 day. If some numbers are left, well... it's getting very hard to test them. I will start a sieve for the next 4 after the first one finishes; that sieve-speed is significantly slower (About 7Mp/sec), but will finish in reasonable time too. After that, I think I will let it go.

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