Other Maths Puzzle Numerical Ability

what is the largest prime no that is stored in 7 bit pattern

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64+32+16+8+4+2+1=127 which is a prime no
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can u plz explain this ans
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(1111111)base2 =(127) base 10
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i just tried for maximum no all 7 bits 1111111 =127 which is prime
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Many early writers felt that the numbers of the form 2n-1 were prime for all primes n, but in 1536 Hudalricus Regius showed that 211-1 = 2047 was not prime (it is 23.89). By 1603 Pietro Cataldi had correctly verified that 217-1 and 219-1 were both prime, but then incorrectly stated 2n-1 was also prime for 23, 29, 31 and 37. In 1640 Fermat showed Cataldi was wrong about 23 and 37; then Euler in 1738 showed Cataldi was also wrong about 29. Sometime later Euler showed Cataldi's assertion about 31 was correct.
Enter French monk Marin Mersenne (1588-1648). Mersenne stated in the preface to his Cogitata Physica-Mathematica (1644) that the numbers 2n-1 were prime for

n = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257
and were composite for all other positive integers n < 257. Mersenne's (incorrect) conjecture fared only slightly better than Regius', but still got his name attached to these numbers.
Definition: When 2n-1 is prime it is said to be a Mersenne prime.
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