Brain Teasers
3-7-31-?-8191-131071
What number is missing from the series?
3-7-31-___-8191-131071-...
3-7-31-___-8191-131071-...
Hint
These are special prime numbers.Answer
127These are the first six Mersenne primes. Mersenne primes are prime numbers of the form 2^p - 1 where p is a prime number.
3 = 2^2 - 1
7 = 2^3 - 1
31 = 2^5 - 1
127 = 2^7 - 1
8191 = 2^13 - 1
131071 = 2^17 - 1
Mersenne prime candidates are often the targets in searches for record-breaking prime numbers.
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Comments
What about 2047?
2^11 - 1
2^11 - 1
2047 = 23 x 89
It's a composite number, not a prime number.
It's a composite number, not a prime number.
"Mersenne primes are prime numbers of the form 2^p - 1 where p is a prime number."
I can see that 2047 isn't prime, so perhaps this definition needs to be revised? (Since 11 is prime, and 2^11 - 1 is not prime).
Fun teaser!
I can see that 2047 isn't prime, so perhaps this definition needs to be revised? (Since 11 is prime, and 2^11 - 1 is not prime).
Fun teaser!
To Paladin: the given definition of Mersenne primes is accurate. It doesn't require every number of the form 2^p-1 (where p is prime) to be prime, it simply defines the *prime* numbers of that form to be Mersenne primes.
Read it carefully, I think you'll agree the definition is complete and correct.
Read it carefully, I think you'll agree the definition is complete and correct.
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