mersenneforum.org Smarandache semiprimes
 Register FAQ Search Today's Posts Mark Forums Read

 2010-04-01, 03:33 #1 sean     Aug 2004 New Zealand 13·17 Posts Smarandache semiprimes Sequence A046461 Sloane's OEIS, about finding semiprime Smarandache numbers (concatenation the positive integers, Sm(11)=1234567891011, etc.). The known values this sequence are 3, 4, 7, 34, 97. For example, Sm(34) = 2 * 6172839455055606570758085909601061116212631364146515661667. Further searching indicates the only other possible members below 2300, are: Code: Sm(631) Sm(691) Sm(859) Sm(1033) Sm(1051) Sm(1291) Sm(1651) Sm(1657) Sm(1831) Sm(1951) Sm(2041) Sm(2047) Sm(2107) Finding a factor any these numbers sufficient (after determing cofactor primality etc.) determine they are the sequence. I've run 100 ecm curves with b1=10000 each candidate, but nothing with higher limits.
 2010-04-01, 03:36 #2 sean     Aug 2004 New Zealand 13·17 Posts Hmm, for some reason the forum i.s losing two letter words like i.s from m.y posts.
2010-04-01, 13:59   #3
EdH

"Ed Hall"
Dec 2009

354610 Posts

Quote:
 Originally Posted by sean Hmm, for some reason the forum i.s losing two letter words like i.s from m.y posts.
I suspect (and hope) this (and other anomalies) will only annoy today...

 2010-04-01, 14:21 #4 CRGreathouse     Aug 2006 2·11·271 Posts Ugh, ,base,-sequences. I'll take Sm(631) t.o 250,000.
 2010-04-01, 15:15 #5 kar_bon     Mar 2006 Germany 2×1,433 Posts Some weeks ago i begun to make a summary-page for Smarandache-type sequences but not yet time to complete everything and the FactorDB-issue for small numbers is annoying,too. See here for Smarandache- and Reverse-Smarandache-sequences.
 2010-04-01, 16:59 #6 Jens K Andersen     Feb 2006 Denmark 3468 Posts PrimeForm/GW has found Sm(5053) = 133283 * prp19099. I'm not attempting to prove the prp.
2010-04-01, 17:50   #7
CRGreathouse

Aug 2006

2·11·271 Posts

Quote:
 Originally Posted by CRGreathouse Ugh, ,base,-sequences. I'll take Sm(631) t.o 250,000.
If nothing goes wrong, I'll have it done through 35 digits (B1 = 1,000,000) tomorrow.

 2010-04-02, 12:38 #8 Jens K Andersen     Feb 2006 Denmark 2·5·23 Posts Sm(9706) = 2 * prp37716, found by PrimeForm/GW.
 2010-04-02, 12:39 #9 CRGreathouse     Aug 2006 2·11·271 Posts Sm(631) = 414941628631826493984534937401473 * C1752 Working on Sm(691) now. Last fiddled with by CRGreathouse on 2010-04-02 at 13:15
 2010-04-05, 19:58 #10 sean     Aug 2004 New Zealand 13×17 Posts Many thanks for the Sm(631) and the results for higher n. In a few days I will submit some extra comments on the OEIS entry.
2010-04-05, 21:47   #11
CRGreathouse

Aug 2006

2×11×271 Posts

Quote:
 Originally Posted by sean Many thanks for the Sm(631) and the results for higher n. In a few days I will submit some extra comments on the OEIS entry.
It would be really nice to find the next term, but that's going to take more than "a few days" unless you get a lot more people.

 Similar Threads Thread Thread Starter Forum Replies Last Post Batalov And now for something completely different 90 2018-06-15 01:48 rogue And now for something completely different 5 2016-07-18 14:33 rogue And now for something completely different 25 2016-01-01 17:07 Hian Homework Help 15 2011-05-29 23:48 robert44444uk Math 34 2007-07-19 17:23

All times are UTC. The time now is 14:59.

Thu Jan 28 14:59:25 UTC 2021 up 56 days, 11:10, 1 user, load averages: 2.67, 3.09, 2.94