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2005-01-25, 21:57
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#1 |
Jan 2005
Transdniestr
1F716 Posts |
Carmichael question
Hello,
Just curious if there's a formula for generating Carmichael numbers with >= 4 prime factors. One 3 factor formula is (6a+1) x (12a+1) x (18a+1) Thanks, Grandpa |
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2005-01-27, 23:18
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#2 |
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Oct 2004
32 Posts |
Indeed, there is.
In 1939 J. Chernick introduced the formula U_k(m) = (6m+1) x (12m+1) x Product[i=1..k-2, (9 x 2^i x m + 1)] is a carmichael number with k factors if all factors are prime. A new algorithm for constructing large carmichael numbers (PDF file, 321 kB) Unbelievable, a carmichael number with 5104 factors... Thanks for the question! 
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2005-01-28, 02:02
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#3 |
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Jan 2005
Transdniestr
503 Posts |
Wow, I got more than I asked for.
 Thanks again, Yogi
Last fiddled with by grandpascorpion on 2005-01-28 at 02:03 |
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2005-01-28, 03:12
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#4 |
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Jan 2005
Transdniestr
7678 Posts |
Actually in that paper Yogi, the authors found Carmichaels with up to 1101518
factors (16m+ digits!) |
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