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Old 2008-11-04, 17:36   #1
petrw1
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Default Mersenne Observation....

I manually inspected up to 10,000 and noticed that in EVERY case when a factor of a mersenne number is used as an exponent it too has a factor and has a relatively small factor.

Example
2^11-1 has a factor of 23
2^23-1 has a factor of 47
2^47-1 has a factor of 13367
2^29-1 has a factor of 233
2^233-1 has a factor of 1399

Is this coincidence OR a characteritic of Mersenne numbers OR ... ?
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Old 2008-11-04, 18:09   #2
R.D. Silverman
 
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Quote:
Originally Posted by petrw1 View Post
I manually inspected up to 10,000 and noticed that in EVERY case when a factor of a mersenne number is used as an exponent it too has a factor and has a relatively small factor.

Example
2^11-1 has a factor of 23
2^23-1 has a factor of 47
2^47-1 has a factor of 13367
2^29-1 has a factor of 233
2^233-1 has a factor of 1399

Is this coincidence ?
Ask yourself: What is the probability that 2^p-1 does NOT have a factor?
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Old 2008-11-04, 18:36   #3
ATH
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Quote:
Originally Posted by R.D. Silverman View Post
Ask yourself: What is the probability that 2^p-1 does NOT have a factor?
There is 1229 primes under 10,000 but only 22 mersenne primes with p<10000.
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Old 2008-11-04, 19:14   #4
petrw1
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To R.D.S. and ATH.

Yes, my first instinct agrees with you.
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Old 2008-11-04, 19:23   #5
Jens K Andersen
 
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2^11-1 = 23*89.
2^89-1 is prime.
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Old 2008-11-04, 20:27   #6
petrw1
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Quote:
Originally Posted by Jens K Andersen View Post
2^11-1 = 23*89.
2^89-1 is prime.
Case closed.
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