20081101, 19:30  #1 
May 2004
New York City
1000010001000_{2} Posts 
Strings of Digits
Where is the longest string of consecutive 0's in a known prime?
What about 1's, 2's, 3's, etc.? What if we restrict to the known Mersenne primes? 
20081101, 19:38  #2 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
1011111100011_{2} Posts 

20081101, 19:52  #3  
"Robert Gerbicz"
Oct 2005
Hungary
3·5·97 Posts 
Quote:
and searching for 10^ we can get probably the best known solutions for digit=0 and 9: p=98035*10^196070+1 containing 196069 consecutive 0's. q=99*10^1396701 containing 139670 consecutive 9's. Since both of them are on the top5000 list, it is possible to check remaining primes on the list, if there is a better solution or not. 

20081101, 20:38  #4  
May 2004
New York City
2^{3}·23^{2} Posts 
Quote:
all bets but 1111111........1111111 are off ! 

20081101, 23:32  #5 
Feb 2006
Denmark
2×5×23 Posts 
n is the largest number of consecutive digits d in the 46 known Mersenne primes 2^p1 with index m=1..46.
d n m p 0 9 46 43112609 1 9 43 30402457 2 8 40 20996011 3 8 40 20996011 4 7 43 30402457 4 7 45 37156667 4 7 46 43112609 5 7 39 13466917 5 7 41 24036583 5 7 43 30402457 5 7 44 32582657 5 7 45 37156667 5 7 46 43112609 (3 times) 6 7 42 25964951 6 7 44 32582657 6 7 46 43112609 7 7 43 30402457 7 7 45 37156667 (2 times) 7 7 46 43112609 8 8 43 30402457 9 8 39 13466917 
20081102, 00:08  #6 
Feb 2006
Denmark
2·5·23 Posts 
Fot other digits than 0 and 9, the best I could spot in the complete Prime Pages database is (8*10^110838*10^1003+9)/9 which starts with 10080 8's. That would be easy to beat with a new prime.

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