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2010-12-24, 12:08   #320
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

2·5·839 Posts

Quote:
 Originally Posted by lorgix Ok, not following. Explanation? Anyway, here are the primes. Should be it for b= 1301 - 1400.
the ones on the diagonal only happen when it's multiplied an even amount of times if not it's on the rim, this is a table of modulo 6 * modulo 6 = modulo 6

the ones highlighted are the only ones b^b can hit so k values are determined but what multiples of these fit things like 6n for 6n+1 on the k*b^b+1 side.

2010-12-24, 16:07   #321
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

2×5×839 Posts

Quote:
 Originally Posted by science_man_88 the ones on the diagonal only happen when it's multiplied an even amount of times if not it's on the rim, this is a table of modulo 6 * modulo 6 = modulo 6 the ones highlighted are the only ones b^b can hit so k values are determined but what multiples of these fit things like 6n for 6n+1 on the k*b^b+1 side.
by*

 2011-01-01, 12:58 #322 lorgix     Sep 2010 Scandinavia 3·5·41 Posts I've recently started factoring numbers of the form k*b^b+1. All results are in factordb. Numbers k*b^b+1 with b and k =<60 , that aren't completely factored: (sorted by number of digits in composite, then b) (These range from c95-c108) Code: 6*56^56+1 29*56^56+1 44*58^58+1 54*58^58+1 57*59^59+1 8*60^60+1 48*59^59+1 2*58^58+1 34*58^58+1 27*59^59+1 11*59^59+1 40*60^60+1 44*59^59+1 43*60^60+1 47*60^60+1 54*60^60+1 17*57^57+1 54*57^57+1 13*58^58+1 15*58^58+1 3*59^59+1 38*59^59+1 10*57^57+1 46*60^60+1 14*58^58+1 56*59^59+1 23*58^58+1 23*59^59+1 50*60^60+1 55*60^60+1 Numbers k*b^b+1 with b and k =<75 , that have no known factors: (sorted by b, then k) Code: 10*57^57+1 7*62^62+1 12*62^62+1 3*66^66+1 28*66^66+1 21*68^68+1 24*69^69+1 49*70^70+1 68*72^72+1 46*73^73+1 18*74^74+1 4*75^75+1 30*75^75+1
2011-01-07, 11:51   #323
lorgix

Sep 2010
Scandinavia

3·5·41 Posts

This should be it for k= 2-12000, b= 1401-1500.

I've also continued factoring k*b^b+1, for small k & b.

All results are in factordb.

Particularly interesting is that 10*57^57+1 still has no known factor.
Attached Files
 kbb1500.zip (2.0 KB, 159 views)

 2011-02-12, 17:51 #324 lorgix     Sep 2010 Scandinavia 3·5·41 Posts I've continued factoring numbers k*b^b+1. I've given potential semi-primes a little extra attention. I seem to be the only one interested, but just in case I'm off by one or more; Here's the most interesting find yet: 7*62^62+1 = p54*p59 p54 = 342564991367278926452734188075388370069540741869652959 p59 = 27456160883590352150849440385563209334798961258762792120351 Poly used: Code: R0: -4072110212622119757654 R1: 456888846229 A0: 10870242064247069137720966187 A1: 1759025599381186974019929 A2: -14527882120011543621 A3: -254910630810921 A4: 1014358042 A5: 8400 skew 113672.30, size 1.376e-010, alpha -7.724, combined = 9.094e-010 rroots = 5 Also noteworthy: Code: 10*57^57+1 = p48*p54 101*54^54+1 = p46*p51 All my results are in factordb.
 2012-09-16, 17:00 #325 3.14159     May 2010 Prime hunting commission. 110100100002 Posts Will try and extend this to b = 1700. Using k = 1 ~ 15000. Code: 1501: 8160, 13086 1502: 4719, 8077, 14358 1503: 1090 Last fiddled with by 3.14159 on 2012-09-16 at 17:32
2016-04-09, 17:45   #326
lorgix

Sep 2010
Scandinavia

3·5·41 Posts

I checked the entire area 2≤k≤30030, 3≤b≤2310 plus and minus one.
Some of the very smallest ones are missing due to the way MultiSieve works.

I have some factors, should anyone want to verify.

Full disclosure: This was done on a 2500K overclocked to 4.2 GHz. It has been perfectly stable for months on end. pfgw didn't report any rounding errors, but there may well be errors of some form or another.

The file contains about 164 thousand primes.
Attached Files
 kbb.7z (291.6 KB, 109 views)

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