A minor point, but it has not been proven that it is computationally infeasible to break midern cryptography. We don't even know if factoring and discrete logarithm, for instance, are NP-complete. (Nor, famously, if P = NP or not.)
Why? It's not as if doing the verification with different algorithms will lessed the probability of a mistake; a quick Google search shows that Glucas is a deterministic algorithm for testing primality of Mersenne numbers.
I can't parse that, so I'll assume you mean that "real men" measure the distance from the water beneath the bridge to one end of the bridge. It seems to me that these same "real men" would consider the Millau bridge to be taller than the Royal Gorge Bridge as well; the bridge has a length of 2.5km, and a nonnegative height in metres. Thus, the farthest end of the bridge from the river Tarn is at least 1.25km, so the distance from the Tarn to this farthest end of the bridge is at least 1.25km. Which beats the hell out of the Royal Gorge Bridge.
I get the idea that walking the length of this bridge is somewhat impractical (not to mention hazardous to the health; imagine the kind of pollution that might settle atop that bridge on a busy day with calm weather.)
We are measuring the height of the bridge, not the maximum vertical distance between any point on the bridge and the ground beneath. The Royal Gorge Bridge appears to be a relatively short structure suspending a surface; certainly nothing on the order of hundreds of feet in height.
The series sum(i=2..infinity) 1/(p_i - p_(i-1)), where p_i is the ith smallest prime, does not converge. Euler showed that sum(i=1..infinity) 1/p_i = 1/2 + sum(i=2..infinity) 1/p_i does not converge; since p_i is positive and increasing for all i, it follows that 0 < p_i - p_(i-1) < p_i, so sum(i=2..infinity) 1/(p_i - p_(i-1)) diverges by the comparison test.
We can go even further: this result also shows that even limit_(i->infinity) 1/(p_i - p_(i-1)) diverges; there are infinitely many twin primes (hence infinitely many terms in this sequence equal 1/2), but for any n, we can find a pair of adjacent primes who are separated by at least n (so, if the limit exists, it must be 0). Since limits are unique, and we have found two distinct values of limit_(i->infinity) 1/(p_i - p_(i-1)), the limit does not exist. (There are also proofs that lim_(i->infinity) 1/(p_i - p_(i-1)) does not exist which rely on smaller hammers than the twin prime theorem, but I do not know them.)
Thus, I find it unlikely that the fdiv bug was discovered as a result of someone trying to prove (or rather, find strong evidence) that the sum you mentioned converged.
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A minor point, but it has not been proven that it is computationally infeasible to break midern cryptography. We don't even know if factoring and discrete logarithm, for instance, are NP-complete. (Nor, famously, if P = NP or not.)
Why? It's not as if doing the verification with different algorithms will lessed the probability of a mistake; a quick Google search shows that Glucas is a deterministic algorithm for testing primality of Mersenne numbers.
I can't parse that, so I'll assume you mean that "real men" measure the distance from the water beneath the bridge to one end of the bridge. It seems to me that these same "real men" would consider the Millau bridge to be taller than the Royal Gorge Bridge as well; the bridge has a length of 2.5km, and a nonnegative height in metres. Thus, the farthest end of the bridge from the river Tarn is at least 1.25km, so the distance from the Tarn to this farthest end of the bridge is at least 1.25km. Which beats the hell out of the Royal Gorge Bridge.
I get the idea that walking the length of this bridge is somewhat impractical (not to mention hazardous to the health; imagine the kind of pollution that might settle atop that bridge on a busy day with calm weather.)
We are measuring the height of the bridge, not the maximum vertical distance between any point on the bridge and the ground beneath. The Royal Gorge Bridge appears to be a relatively short structure suspending a surface; certainly nothing on the order of hundreds of feet in height.
The series sum(i=2..infinity) 1/(p_i - p_(i-1)), where p_i is the ith smallest prime, does not converge. Euler showed that sum(i=1..infinity) 1/p_i = 1/2 + sum(i=2..infinity) 1/p_i does not converge; since p_i is positive and increasing for all i, it follows that 0 < p_i - p_(i-1) < p_i, so sum(i=2..infinity) 1/(p_i - p_(i-1)) diverges by the comparison test.
We can go even further: this result also shows that even limit_(i->infinity) 1/(p_i - p_(i-1)) diverges; there are infinitely many twin primes (hence infinitely many terms in this sequence equal 1/2), but for any n, we can find a pair of adjacent primes who are separated by at least n (so, if the limit exists, it must be 0). Since limits are unique, and we have found two distinct values of limit_(i->infinity) 1/(p_i - p_(i-1)), the limit does not exist. (There are also proofs that lim_(i->infinity) 1/(p_i - p_(i-1)) does not exist which rely on smaller hammers than the twin prime theorem, but I do not know them.)
Thus, I find it unlikely that the fdiv bug was discovered as a result of someone trying to prove (or rather, find strong evidence) that the sum you mentioned converged.