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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) Just showing those entries submitted by 'Beedassy': (Click here to show all) The fair approximation log 2/3 = log 5/7 between the successive digits of prime 2357 is a direct consequence of the observation that 2^{7} is close to 5^{3}. [Beedassy]The number with each prime digit d repeated d times and the whole sandwiched between two blocks of prime 2357, is prime: 2357223335555577777772357. [Beedassy] Replacing each prime digit in 2357 by its complement forms the prime 8753. Note that combining the two primes by interweaving their digits forms another prime: 82735537. [Beedassy] The sum of 2357 and its successive righttruncations (2357 + 235 + 23 + 2 + 0) is prime, and so is the sum of the successive deleted digits (0 + 7 + 5 + 3 + 2). [Beedassy] 2^{p7} + 3^{p5} + 5^{p3} + 7^{p2} is prime, where p_{n} is the nth prime. [Beedassy] The double Mersenne numbers M_{Mp} = 2^{Mp}  1, (where M_{p} = 2^{p}  1) are primes only for p = 2, 3, 5, 7. [Beedassy] Adding the prime digits (2, 3, 5, 7) either to all primes with a prime number of distinct prime digits (23, 37, 53, 73, 257, 523) or to all nonprimes with a nonprime number of distinct prime digits (2375, 2537, 2573, 2735, 3275, 3572, 3725, 3752, 5327, 5372, 5723, 5732, 7235, 7325, 7352, 7532 ) forms a prime in each case (983 ; 76159) the reversal of whose product is also prime (79246847). [Beedassy] 2357 can be expressed as the repdigit sum of its (prime) digits: 2222 + 3 + 55 + 77. Note that the latter summands concatenate, in some appropriate order, into a prime, in three different ways all starting with "55": 553222277, 552222773, 557722223. [Beedassy] The alternating productseries 235*7 +/ 23*57 /+ 2*357 +/ 23*5*7 /+ 2*35*7 +/ 2*3*57 /+ 2*3*5*7 yield prime sums (2689, 601) whose concatenations (2689601, 6012689) are also prime. [Beedassy] The reverse concatenation of the two prime derangements (5273 and 7523) of 2357 is prime: 75235273. Note that sandwiching the latter between two blocks of prime 2357, followed by halving at the middle yields a new pair of primes (23577523 ; 52732357 ) both remaining prime when every digit is replaced by its respective complement (87533587 ; 58378753). [Beedassy] Replacing from the left the first digits in 2357 by their partial sums forms a succession of four primes,viz., 2357, 557, 107, 17. Note that the reversals of both semiprimes 2357*557 and 107*17 are prime (9482131, 9181). [Beedassy]
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