Question

prove that if $p$ is a prime number, then $\sqrt{p}$ is an irrational number.

score 10.9k · Answer 1 · 2018-03-08 12:12:59

10.9k

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prove that if $p$ is a prime number, then $\sqrt{p}$ is an irrational number.

Published on 08 Mar 2018 - 12:12

score 435 · Answer 2 · 2026-03-25 01:17:01

435

Views

Manual factorization of a large number in hexadecimal format

Published on 25 Mar 2026 - 1:17

score 59 · Answer 3 · 2026-03-22 07:49:08

59

Views

Can you propose a conjectural $\text{Upper bound}(x)$ for the counting function of a sequence of primes arising from the Eratosthenes sieve?

Published on 22 Mar 2026 - 7:49

score 42 · Answer 4 · 2026-03-25 06:30:33

42

Views

Difference in total number of positive integers $x, y, z$ determined from an equation.

Published on 25 Mar 2026 - 6:30

score 39 · Answer 5 · 2026-03-25 12:45:38

39

Views

A simple modular arithmetic problem

Published on 25 Mar 2026 - 12:45

score 285 · Answer 6 · 2026-03-25 19:25:28

285

Views

Solve the following equation where $p$ is prime: $ p^n + 144 = m^2 $

Published on 25 Mar 2026 - 19:25

score 266 · Answer 7 · 2018-03-09 08:57:35

266

Views

Conjecture on product of first $n$ primes.

Published on 09 Mar 2018 - 8:57

score 60 · Answer 8 · 2026-03-25 17:24:34

60

Views

The asymptotic behaviour of an arithmetic function related to the $K$-function

Published on 25 Mar 2026 - 17:24

score 50 · Answer 9 · 2018-03-10 02:24:17

50

Views

Are there composite numbers that can stump this Pocklington variant?

Published on 10 Mar 2018 - 2:24

score 47 · Answer 10 · 2026-03-23 12:12:04

47

Views

Show that for any open subset of $\Bbb R$, there is a fraction with prime terms that belongs to it

Published on 23 Mar 2026 - 12:12

score 71 · Answer 11 · 2026-03-25 05:01:11

71

Views

Combinations of exponents resulting in prime numbers

Published on 25 Mar 2026 - 5:01

score 185 · Answer 12 · 2026-03-22 12:39:37

185

Views

Investigating natural numbers in relations with prime numbers

Published on 22 Mar 2026 - 12:39

score 222 · Answer 13 · 2026-03-25 04:44:23

222

Views

An approximation for $1\leq n\leq N$ of the number of solutions of $2^{\pi(n)}\equiv 1\text{ mod }n$, where $\pi(x)$ is the prime-counting function

Published on 25 Mar 2026 - 4:44

score 87 · Answer 14 · 2026-03-25 06:17:38

87

Views

DLP - method for calculating order

Published on 25 Mar 2026 - 6:17

score 125 · Answer 15 · 2026-03-22 21:20:28

125

Views

Primes formed by concatenating the mersenne numbers from $2^2-1$ to $2^n-1$

Published on 22 Mar 2026 - 21:20

List Question

prove that if $p$ is a prime number, then $\sqrt{p}$ is an irrational number.

Manual factorization of a large number in hexadecimal format

Can you propose a conjectural $\text{Upper bound}(x)$ for the counting function of a sequence of primes arising from the Eratosthenes sieve?

Difference in total number of positive integers $x, y, z$ determined from an equation.

A simple modular arithmetic problem

Solve the following equation where $p$ is prime: $ p^n + 144 = m^2 $

Conjecture on product of first $n$ primes.

The asymptotic behaviour of an arithmetic function related to the $K$-function

Are there composite numbers that can stump this Pocklington variant?

Show that for any open subset of $\Bbb R$, there is a fraction with prime terms that belongs to it

Combinations of exponents resulting in prime numbers

Investigating natural numbers in relations with prime numbers

An approximation for $1\leq n\leq N$ of the number of solutions of $2^{\pi(n)}\equiv 1\text{ mod }n$, where $\pi(x)$ is the prime-counting function

DLP - method for calculating order

Primes formed by concatenating the mersenne numbers from $2^2-1$ to $2^n-1$

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