Question

Checking the Harald Helfgott proof of the little Goldbach conjecture without a public release of numerical checks?

score 2.3k · Answer 1 · 2013-10-05 20:25:32

2.3k

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Checking the Harald Helfgott proof of the little Goldbach conjecture without a public release of numerical checks?

Published on 05 Oct 2013 - 20:25

score 2.5k · Answer 2 · 2013-10-06 05:16:15

2.5k

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A conjectural closed form for $\sum\limits_{n=0}^\infty\frac{n!\,(2n)!}{(3n+2)!}$

Published on 06 Oct 2013 - 5:16

score 553 · Answer 3 · 2026-03-29 07:29:19

553

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A conjecture $\int_{-\infty}^\infty\frac{\arctan e^x}{\cosh x}\cdot\frac{\tanh\frac{x}2}{x}dx\stackrel?=\frac\pi2\ln2$

Published on 29 Mar 2026 - 7:29

score 372 · Answer 4 · 2013-10-10 17:58:40

372

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Integral $\int_0^\infty\frac{dx}{\frac{x^4-1}{x\cos(\pi\ln x)+1}+2x^2+2}$

Published on 10 Oct 2013 - 17:58

score 3.6k · Answer 5 · 2026-03-29 10:49:03

3.6k

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Integral $\int_1^\infty\operatorname{arccot}\left(1+\frac{2\pi}{\operatorname{arcoth}x-\operatorname{arccsc}x}\right)\frac{\mathrm dx}{\sqrt{x^2-1}}$

Published on 29 Mar 2026 - 10:49

score 730 · Answer 6 · 2026-03-27 03:44:10

730

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Simplify $\frac{_3F_2\left(\frac{1}{2},\frac{3}{4},\frac{5}{4};1,\frac{3}{2};\frac{3}{4}\right)}{\Pi\left(\frac{1}{4}\big|\frac{1}{\sqrt{3}}\right)}$

Published on 27 Mar 2026 - 3:44

score 469 · Answer 7 · 2013-10-11 22:11:19

469

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Conjecture $\int_0^1\frac{\ln\left(\ln^2x+\arccos^2x\right)}{\sqrt{1-x^2}}dx\stackrel?=\pi\,\ln\ln2$

Published on 11 Oct 2013 - 22:11

score 129 · Answer 8 · 2026-03-26 04:51:42

129

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A challenging non homogenous fractional inequality.

Published on 26 Mar 2026 - 4:51

score 142 · Answer 9 · 2013-10-15 11:07:42

142

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What are the recent advancements in mathematics that an undergraduate can understand?

Published on 15 Oct 2013 - 11:07

score 767 · Answer 10 · 2013-10-17 18:02:25

767

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Totient summatory function

Published on 17 Oct 2013 - 18:02

score 203 · Answer 11 · 2013-10-19 13:24:43

203

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What's wrong with my conjecture?

Published on 19 Oct 2013 - 13:24

score 781 · Answer 12 · 2013-10-19 16:46:14

781

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Prove $_4F_3(1/8,3/8,5/8,7/8;1/4,1/2,3/4;1/2)=\frac{\sqrt{2-\sqrt2+\sqrt{2-\sqrt2}}+\sqrt{2+\sqrt2+\sqrt{2+\sqrt2}}}{2\,\sqrt2}$

Published on 19 Oct 2013 - 16:46

score 618 · Answer 13 · 2013-10-20 12:54:15

618

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My conjecture on almost integers.

Published on 20 Oct 2013 - 12:54

score 5.5k · Answer 14 · 2013-10-24 20:22:06

5.5k

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Conjecture $\int_0^1\frac{dx}{\sqrt[3]x\,\sqrt[6]{1-x}\,\sqrt{1-x\left(\sqrt{6}\sqrt{12+7\sqrt3}-3\sqrt3-6\right)^2}}=\frac\pi9(3+\sqrt2\sqrt[4]{27})$

Published on 24 Oct 2013 - 20:22

score 7.3k · Answer 15 · 2013-10-27 05:23:26

7.3k

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Conjecture $\int_0^1\frac{\mathrm dx}{\sqrt{1-x}\ \sqrt[4]x\ \sqrt[4]{2-x\,\sqrt3}}\stackrel?=\frac{2\,\sqrt2}{3\,\sqrt[8]3}\pi$

Published on 27 Oct 2013 - 5:23

List Question

Checking the Harald Helfgott proof of the little Goldbach conjecture without a public release of numerical checks?

A conjectural closed form for $\sum\limits_{n=0}^\infty\frac{n!\,(2n)!}{(3n+2)!}$

A conjecture $\int_{-\infty}^\infty\frac{\arctan e^x}{\cosh x}\cdot\frac{\tanh\frac{x}2}{x}dx\stackrel?=\frac\pi2\ln2$

Integral $\int_0^\infty\frac{dx}{\frac{x^4-1}{x\cos(\pi\ln x)+1}+2x^2+2}$

Integral $\int_1^\infty\operatorname{arccot}\left(1+\frac{2\pi}{\operatorname{arcoth}x-\operatorname{arccsc}x}\right)\frac{\mathrm dx}{\sqrt{x^2-1}}$

Simplify $\frac{_3F_2\left(\frac{1}{2},\frac{3}{4},\frac{5}{4};1,\frac{3}{2};\frac{3}{4}\right)}{\Pi\left(\frac{1}{4}\big|\frac{1}{\sqrt{3}}\right)}$

Conjecture $\int_0^1\frac{\ln\left(\ln^2x+\arccos^2x\right)}{\sqrt{1-x^2}}dx\stackrel?=\pi\,\ln\ln2$

A challenging non homogenous fractional inequality.

What are the recent advancements in mathematics that an undergraduate can understand?

Totient summatory function

What's wrong with my conjecture?

Prove $_4F_3(1/8,3/8,5/8,7/8;1/4,1/2,3/4;1/2)=\frac{\sqrt{2-\sqrt2+\sqrt{2-\sqrt2}}+\sqrt{2+\sqrt2+\sqrt{2+\sqrt2}}}{2\,\sqrt2}$

My conjecture on almost integers.

Conjecture $\int_0^1\frac{dx}{\sqrt[3]x\,\sqrt[6]{1-x}\,\sqrt{1-x\left(\sqrt{6}\sqrt{12+7\sqrt3}-3\sqrt3-6\right)^2}}=\frac\pi9(3+\sqrt2\sqrt[4]{27})$

Conjecture $\int_0^1\frac{\mathrm dx}{\sqrt{1-x}\ \sqrt[4]x\ \sqrt[4]{2-x\,\sqrt3}}\stackrel?=\frac{2\,\sqrt2}{3\,\sqrt[8]3}\pi$

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