Fibonacci primes vs Mersenne primes
0
$begingroup$
It seems that only 34 Fibonacci primes are known while 54 Mersenne primes are known, while Fibonacci numbers are sparser than Mersenne numbers. Compare
https://en.wikipedia.org/wiki/Fibonacci_prime
and
https://en.wikipedia.org/wiki/Mersenne_prime
Is there a heuristic argument to explain this discrepancy?
prime-numbers fibonacci-numbers mersenne-numbers
asked Jan 25 at 23:03
Patrick SolePatrick Sole
1227
$endgroup$
add a comment |
0
$begingroup$
It seems that only 34 Fibonacci primes are known while 54 Mersenne primes are known, while Fibonacci numbers are sparser than Mersenne numbers. Compare
https://en.wikipedia.org/wiki/Fibonacci_prime
and
https://en.wikipedia.org/wiki/Mersenne_prime
Is there a heuristic argument to explain this discrepancy?
prime-numbers fibonacci-numbers mersenne-numbers
asked Jan 25 at 23:03
Patrick SolePatrick Sole
1227
$endgroup$
1
$begingroup$
We have better algorithms for testing primality of Mersenne numbers, see the Lucas–Lehmer primality test
$endgroup$
– Wojowu
Jan 25 at 23:13
$begingroup$
I do not know whether probable fibonacci primes are known. But the other possibility is that there simply are less fibonacci primes upto the same limit. That can be because of the structure of the numbers. Do you have any reason to assume that the number of primes should approximately coincide ?
$endgroup$
– Peter
Jan 26 at 12:58
$begingroup$
There is no reason to conjecture that the two numbers should coincide. Given that Mersenne numbers grow faster there should be less of them.
$endgroup$
– Patrick Sole
Jan 26 at 16:45
add a comment |
0
0
0
$begingroup$
It seems that only 34 Fibonacci primes are known while 54 Mersenne primes are known, while Fibonacci numbers are sparser than Mersenne numbers. Compare
https://en.wikipedia.org/wiki/Fibonacci_prime
and
https://en.wikipedia.org/wiki/Mersenne_prime
Is there a heuristic argument to explain this discrepancy?
prime-numbers fibonacci-numbers mersenne-numbers
asked Jan 25 at 23:03
Patrick SolePatrick Sole
1227
$endgroup$
It seems that only 34 Fibonacci primes are known while 54 Mersenne primes are known, while Fibonacci numbers are sparser than Mersenne numbers. Compare
https://en.wikipedia.org/wiki/Fibonacci_prime
and
https://en.wikipedia.org/wiki/Mersenne_prime
Is there a heuristic argument to explain this discrepancy?
prime-numbers fibonacci-numbers mersenne-numbers
prime-numbers fibonacci-numbers mersenne-numbers
asked Jan 25 at 23:03
Patrick SolePatrick Sole
1227
asked Jan 25 at 23:03
Patrick SolePatrick Sole
1227
asked Jan 25 at 23:03
Patrick SolePatrick Sole
1227
asked Jan 25 at 23:03
Patrick SolePatrick Sole
1227
asked Jan 25 at 23:03
Patrick SolePatrick Sole
1227
1227
1
$begingroup$
We have better algorithms for testing primality of Mersenne numbers, see the Lucas–Lehmer primality test
$endgroup$
– Wojowu
Jan 25 at 23:13
$begingroup$
I do not know whether probable fibonacci primes are known. But the other possibility is that there simply are less fibonacci primes upto the same limit. That can be because of the structure of the numbers. Do you have any reason to assume that the number of primes should approximately coincide ?
$endgroup$
– Peter
Jan 26 at 12:58
$begingroup$
There is no reason to conjecture that the two numbers should coincide. Given that Mersenne numbers grow faster there should be less of them.
$endgroup$
– Patrick Sole
Jan 26 at 16:45
add a comment |
1
$begingroup$
We have better algorithms for testing primality of Mersenne numbers, see the Lucas–Lehmer primality test
$endgroup$
– Wojowu
Jan 25 at 23:13
$begingroup$
I do not know whether probable fibonacci primes are known. But the other possibility is that there simply are less fibonacci primes upto the same limit. That can be because of the structure of the numbers. Do you have any reason to assume that the number of primes should approximately coincide ?
$endgroup$
– Peter
Jan 26 at 12:58
$begingroup$
There is no reason to conjecture that the two numbers should coincide. Given that Mersenne numbers grow faster there should be less of them.
$endgroup$
– Patrick Sole
Jan 26 at 16:45
1
1
$begingroup$
We have better algorithms for testing primality of Mersenne numbers, see the Lucas–Lehmer primality test
$endgroup$
– Wojowu
Jan 25 at 23:13
$begingroup$
We have better algorithms for testing primality of Mersenne numbers, see the Lucas–Lehmer primality test
$endgroup$
– Wojowu
Jan 25 at 23:13
$begingroup$
I do not know whether probable fibonacci primes are known. But the other possibility is that there simply are less fibonacci primes upto the same limit. That can be because of the structure of the numbers. Do you have any reason to assume that the number of primes should approximately coincide ?
$endgroup$
– Peter
Jan 26 at 12:58
$begingroup$
I do not know whether probable fibonacci primes are known. But the other possibility is that there simply are less fibonacci primes upto the same limit. That can be because of the structure of the numbers. Do you have any reason to assume that the number of primes should approximately coincide ?
$endgroup$
– Peter
Jan 26 at 12:58
$begingroup$
There is no reason to conjecture that the two numbers should coincide. Given that Mersenne numbers grow faster there should be less of them.
$endgroup$
– Patrick Sole
Jan 26 at 16:45
$begingroup$
There is no reason to conjecture that the two numbers should coincide. Given that Mersenne numbers grow faster there should be less of them.
$endgroup$
– Patrick Sole
Jan 26 at 16:45
add a comment |
0
active
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1
$begingroup$
We have better algorithms for testing primality of Mersenne numbers, see the Lucas–Lehmer primality test
$endgroup$
– Wojowu
Jan 25 at 23:13
$begingroup$
I do not know whether probable fibonacci primes are known. But the other possibility is that there simply are less fibonacci primes upto the same limit. That can be because of the structure of the numbers. Do you have any reason to assume that the number of primes should approximately coincide ?
$endgroup$
– Peter
Jan 26 at 12:58
$begingroup$
There is no reason to conjecture that the two numbers should coincide. Given that Mersenne numbers grow faster there should be less of them.
$endgroup$
– Patrick Sole
Jan 26 at 16:45