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Old 2013-02-07, 14:34   #1
davar55
 
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Default Mersenne Digits Curiosity

The newly found M48 exponent is of the form 5*1,where * is
a digit sequence. But so is M48 itself of this same form, 5*1.

Is this the first found Mersenne prime which matches its
generating exponent in initial and final digits?
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Old 2013-02-07, 15:25   #2
aketilander
 
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No

M11 1*7
M12 1*7
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Old 2013-02-07, 15:43   #3
ATH
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No:

M107 = 162259276829213363391578010288127
M127 = 170141183460469231731687303715884105727

http://mathworld.wolfram.com/MersennePrime.html

So it is the third one.

Edit: Ops I didn't hit refresh on the thread, I so I didn't notice it was already answered.

Last fiddled with by ATH on 2013-02-07 at 15:43
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Old 2013-02-07, 18:34   #4
ATH
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The possible last 2 digits for 2^p - 1 with prime p is:
07,11,27,47,51,71,87,91 (and 03,31 for p<=5)
and we had them all in the 48 mersenne primes.

The 40 possible last 3 digits are:
Code:
007,047,071,087,111,127,151,191,207,247,271,287,311,327,351,391,407,447,471,487,511,527,551,591,607,647,671,687,711,727,751,791,807,847,871,887,911,927,951,991   (and 003,031 for p<=5)
of those we have yet to find mersenne primes with these endings:

327,391,487,687,807,847,911
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Old 2013-02-07, 19:55   #5
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I searched the decimal digits of M57885161 for strings 00,01,...,99 and then 000,001...999 and so on:

00..99: All appears at least once in the first 702 digits, the last one to appear is "99" at digit 701-702.

000...999: All appears at least once in the first 7658 digits, the last one to appear is "784" at digit 7656-7658.

0000...9999: All appears at least once in the first 122997 digits, the last one to appear is "8990" at digit 122994-122997.

00000...99999: All appears at least once in the first 1206777 digits, the last one to appear is "34411" at digit 1206773-1206777.

000000...999999: All appears at least once in the first 14939172 digits, the last one to appear is "243484" at digit 14939167-14939172.

0000000...9999999: 8249630 of the 10000000 strings occur, the first 5 to NOT occur is "0000002","0000003","0000004","0000008","0000011"

Last fiddled with by ATH on 2013-02-07 at 19:57
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Old 2013-02-07, 20:15   #6
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Somewhat related:

http://www.mersenneforum.org/showthread.php?t=5414
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Old 2013-02-07, 20:16   #7
cmd
 
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Quote:
Originally Posted by ATH View Post
The possible last 2 digits for 2^p - 1 with prime p is:
07,11,27,47,51,71,87,91 (and 03,31 for p<=5)
and we had them all in the 48 mersenne primes.

The 40 possible last 3 digits are:
Code:
007,047,071,087,111,127,151,191,207,247,271,287,311,327,351,391,407,447,471,487,511,527,551,591,607,647,671,687,711,727,751,791,807,847,871,887,911,927,951,991   (and 003,031 for p<=5)
of those we have yet to find mersenne primes with these endings:

327,391,487,687,807,847,911
cmd_sche_M_e
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Old 2013-02-08, 07:55   #8
ET_
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Quote:
Originally Posted by ATH View Post
I searched the decimal digits of M57885161 for strings 00,01,...,99 and then 000,001...999 and so on:

00..99: All appears at least once in the first 702 digits, the last one to appear is "99" at digit 701-702.

000...999: All appears at least once in the first 7658 digits, the last one to appear is "784" at digit 7656-7658.

0000...9999: All appears at least once in the first 122997 digits, the last one to appear is "8990" at digit 122994-122997.

00000...99999: All appears at least once in the first 1206777 digits, the last one to appear is "34411" at digit 1206773-1206777.

000000...999999: All appears at least once in the first 14939172 digits, the last one to appear is "243484" at digit 14939167-14939172.

0000000...9999999: 8249630 of the 10000000 strings occur, the first 5 to NOT occur is "0000002","0000003","0000004","0000008","0000011"
What about 3.1415926535 or 2.7182818284?

Luigi
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Old 2013-02-08, 10:30   #9
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Quote:
Originally Posted by ET_ View Post
What about 3.1415926535 or 2.7182818284?

Luigi
Pi: longest term is 3141592 (only once) starting at digit 6524707.
e: longest term is 2718281 (3 times) starting at digit 1339924 for lowest one.
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Old 2013-02-08, 14:04   #10
Stargate38
 
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Do 8675309, 24972797, and 4198862272 appear anywhere?
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Old 2013-02-08, 15:14   #11
ATH
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Quote:
Originally Posted by Stargate38 View Post
Do 8675309, 24972797, and 4198862272 appear anywhere?
8675309 appear 5 times at 2500006-2500012, 4944089-4944095, 6227890-6227896, 9850482-9850488, 10692120-10692126

24972797 and 4198862272 does not appear.
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