3,348 reputation
2826
bio website
location
age
visits member for 2 years, 10 months
seen 1 hour ago

1d
revised Sorting of prime gaps
added 205 characters in body
1d
revised Sorting of prime gaps
deleted 273 characters in body
Aug
17
revised Sorting of prime gaps
deleted 454 characters in body
Aug
17
revised Examples of advancement in mathematics due to war
added 176 characters in body
Aug
17
answered Examples of advancement in mathematics due to war
Aug
17
revised Sorting of prime gaps
edited body
Aug
17
revised Sorting of prime gaps
added 917 characters in body
Aug
15
comment Closed form of $\int_0^2\frac{1}{2+\sqrt{3\,e^x+3\,e^{-x}-2}}dx$
Mathematica gives $ \int f(x)dx = \int \frac{dx}{2+\sqrt{6\cosh x-2}} = I(x) = (1/6) \left[(2 - \sqrt{-2 + 6 \cosh x}~)\cdot \coth \frac{x}{2} - 2~ i~ E_2((i~ x/2),~ 3) - 4~i ~E_1((i~x/2),~ 3)\right]. $ Using Santosh Linkha's idea, and taking care to take the $\lim_{a\to 0} \int_a^2$ gives the answer in the OP. $E_1,E_2$ are elliptic integrals.
Aug
15
revised Sorting of prime gaps
deleted 360 characters in body
Aug
13
accepted “Probability” of a large integer being prime
Aug
13
accepted Iteration of $x/\log x$
Aug
13
revised Sorting of prime gaps
added 305 characters in body
Aug
13
revised Sorting of prime gaps
added 305 characters in body
Aug
11
asked Sorting of prime gaps
Jul
24
accepted Limit of Sum $\sum \frac{p(k+1) - p(k)}{p(k)^2}$ ? (corrected)
Jul
24
comment Limit of Sum $\sum \frac{p(k+1) - p(k)}{p(k)^2}$ ? (corrected)
Yes, thanks, I don't trust my results that far but the differences were getting small quickly.
Jul
24
revised Limit of Sum $\sum \frac{p(k+1) - p(k)}{p(k)^2}$ ? (corrected)
added 12 characters in body
Jul
24
reviewed Approve suggested edit on Limit of Sum $\sum \frac{p(k+1) - p(k)}{p(k)^2}$ ? (corrected)
Jul
24
asked Limit of Sum $\sum \frac{p(k+1) - p(k)}{p(k)^2}$ ? (corrected)
Jul
20
comment Euclid's proof of the infinitude of primes to prove this question
@MichaelHardy: This is a really nice paper and worth several readings. Thanks for the reference and the surprising answer.