Mersenne Digits Curiosity

davar55 · 2013-02-07, 14:34

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?

aketilander · 2013-02-07, 15:25

No

M11 1*7
M12 1*7

ATH · 2013-02-07, 15:43

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.

ATH · 2013-02-07, 18:34

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

ATH · 2013-02-07, 19:55

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"

Xyzzy · 2013-02-07, 20:15

Somewhat related:

http://www.mersenneforum.org/showthread.php?t=5414

cmd · 2013-02-07, 20:16

Quote:

Originally Posted by ATH

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

ET_ · 2013-02-08, 07:55

Quote:

Originally Posted by ATH

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

kar_bon · 2013-02-08, 10:30

Quote:

Originally Posted by ET_

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.

Stargate38 · 2013-02-08, 14:04

Do 8675309, 24972797, and 4198862272 appear anywhere?

ATH · 2013-02-08, 15:14

Quote:

Originally Posted by Stargate38

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.

2013-02-07, 14:34	#1
davar55 May 2004 New York City 5×7×11² Posts	Mersenne Digits Curiosity The newly found M48 exponent is of the form 51,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?

2013-02-07, 15:43	#3
ATH Einyen Dec 2003 Denmark 6426₈ Posts	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

2013-02-07, 18:34	#4
ATH Einyen Dec 2003 Denmark 2×5²×67 Posts	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

2013-02-07, 19:55	#5
ATH Einyen Dec 2003 Denmark 2·5²·67 Posts	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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2013-02-07, 15:25	#2
aketilander "Åke Tilander" Apr 2011 Sandviken, Sweden 236₁₆ Posts	No M11 17 M12 17

2013-02-07, 20:15	#6
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