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drummers-lowrise
1) Message boards : PrimeSearchTeam message board (Message 130073)
Posted 970 days ago by paolo
https://mathoverflow.net/questions/294527/are-concatenations-of-two-consecutive-mersenne-numbers-which-are-congruent-to-6

https://mathoverflow.net/questions/321020/probable-primes-of-a

I found primes of this type up to k=4*10^5. Can you help me to go further at least up to k=10^6? These primes are formed by concatenating in decreasing order two consecutive Mersenne numbers eg 255127, 12763, 40952047. No prime of this form congruent to 6 mod 7 was found up to k=800.000.
2) Message boards : PrimeSearchTeam message board (Message 130060)
Posted 971 days ago by paolo
Hallo i am searching for primes of the form 10^d*(2^k-1)+2^(k-1)-1 where k is a non negative integer and d is the number of decimal digits of 2^(k-1)-1 eg 12763, 255127, 40952047. Two posts on mathoverflow have received a lot of views because none of these primes up to k=800.000 is congruent to 6 mod 7 and everytime k is a multiple of 43, then k is also of the form 41s+r, with r in the set (1,10,16,18,37). Can you help me to find primes of this form at least up to k=10^6?
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