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Old 2010-04-01, 03:33   #1
sean
 
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Default 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.
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Old 2010-04-01, 03:36   #2
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Hmm, for some reason the forum i.s losing two letter words like i.s from m.y posts.
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Old 2010-04-01, 13:59   #3
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Quote:
Originally Posted by sean View Post
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...
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Old 2010-04-01, 14:21   #4
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Ugh, ,base,-sequences. I'll take Sm(631) t.o 250,000.
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Old 2010-04-01, 15:15   #5
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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.
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Old 2010-04-01, 16:59   #6
Jens K Andersen
 
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PrimeForm/GW has found Sm(5053) = 133283 * prp19099.

I'm not attempting to prove the prp.
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Old 2010-04-01, 17:50   #7
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Quote:
Originally Posted by CRGreathouse View Post
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.
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Old 2010-04-02, 12:38   #8
Jens K Andersen
 
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Sm(9706) = 2 * prp37716, found by PrimeForm/GW.
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Old 2010-04-02, 12:39   #9
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Sm(631) = 414941628631826493984534937401473 * C1752

Working on Sm(691) now.

Last fiddled with by CRGreathouse on 2010-04-02 at 13:15
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Old 2010-04-05, 19:58   #10
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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.
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Old 2010-04-05, 21:47   #11
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Quote:
Originally Posted by sean View Post
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.
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