20130207, 14:34  #1 
May 2004
New York City
3×17×83 Posts 
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? 
20130207, 15:25  #2 
"Åke Tilander"
Apr 2011
Sandviken, Sweden
2×283 Posts 
No
M11 1*7 M12 1*7 
20130207, 15:43  #3 
Einyen
Dec 2003
Denmark
6070_{8} 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 20130207 at 15:43 
20130207, 18:34  #4 
Einyen
Dec 2003
Denmark
6070_{8} 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) 327,391,487,687,807,847,911 
20130207, 19:55  #5 
Einyen
Dec 2003
Denmark
2^{3}·17·23 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 701702. 000...999: All appears at least once in the first 7658 digits, the last one to appear is "784" at digit 76567658. 0000...9999: All appears at least once in the first 122997 digits, the last one to appear is "8990" at digit 122994122997. 00000...99999: All appears at least once in the first 1206777 digits, the last one to appear is "34411" at digit 12067731206777. 000000...999999: All appears at least once in the first 14939172 digits, the last one to appear is "243484" at digit 1493916714939172. 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 20130207 at 19:57 
20130207, 20:15  #6 
"Mike"
Aug 2002
2^{5}·3·5·17 Posts 

20130207, 20:16  #7  
"(^r'°:.:)^n;e'e"
Nov 2008
;t:.:;^
1111100111_{2} Posts 
trust
Quote:


20130208, 07:55  #8  
Banned
"Luigi"
Aug 2002
Team Italia
11315_{8} Posts 
Quote:
Luigi 

20130208, 10:30  #9 
Mar 2006
Germany
5512_{8} Posts 

20130208, 14:04  #10 
"Daniel Jackson"
May 2011
14285714285714285714
2×5^{2}×13 Posts 
Do 8675309, 24972797, and 4198862272 appear anywhere?

20130208, 15:14  #11 
Einyen
Dec 2003
Denmark
2^{3}·17·23 Posts 

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