Newbetuts

If $a, b, c, d$ are natural numbers, such that, $ab = cd$, prove that $a^2 + b^2 + c^2 + d^2$ is a composite number.

$(p\!-\!1\!-\!h)!\,h! \equiv (-1)^{h+1}\!\!\pmod{\! p}\,$ [Wilson Reflection Formula]

If $x$, $y$, $x+y$, and $x-y$ are prime numbers, what is their sum?

Does $\lfloor \sqrt{p} \rfloor$ generate all natural numbers?

Can we remove any prime number with this strange process?

Least prime of the form $38^n+31$

Different ways to prove there are infinitely many primes?

Finding a primitive root of a prime number

$n!$ is never a perfect square if $n\geq2$. Is there a proof of this that doesn't use Chebyshev's theorem?

Efficiently finding two squares which sum to a prime

If $p$ is a prime and $p \mid ab$, then $p \mid a$ or $p \mid b\ $ [Euclid's Lemma]

If a prime $p\mid ab$, then $p\mid a$ or $p\mid b\ $ [Euclid's Lemma]

Infiniteness of non-twin primes.

Why is $1$ not a prime number?

Alternate definition of prime number

Split $n$ into nontrivial factors via a nontrivial square-root of $1\!\pmod{\!n}$

Do Arithmetic Mean and Geometric Mean of Prime Numbers converge?

New posts in prime-numbers

Let $p$ be prime and $(\frac{-3}p)=1$. Prove that $p$ is of the form $p=a^2+3b^2$

Is there possibly a largest prime number?

Does the sum of reciprocals of primes converge?

If $a, b, c, d$ are natural numbers, such that, $ab = cd$, prove that $a^2 + b^2 + c^2 + d^2$ is a composite number.

$(p\!-\!1\!-\!h)!\,h! \equiv (-1)^{h+1}\!\!\pmod{\! p}\,$ [Wilson Reflection Formula]

If $x$, $y$, $x+y$, and $x-y$ are prime numbers, what is their sum?

Does $\lfloor \sqrt{p} \rfloor$ generate all natural numbers?

Can we remove any prime number with this strange process?

Least prime of the form $38^n+31$

Different ways to prove there are infinitely many primes?

Finding a primitive root of a prime number

$n!$ is never a perfect square if $n\geq2$. Is there a proof of this that doesn't use Chebyshev's theorem?

Efficiently finding two squares which sum to a prime

If $p$ is a prime and $p \mid ab$, then $p \mid a$ or $p \mid b\ $ [Euclid's Lemma]

If a prime $p\mid ab$, then $p\mid a$ or $p\mid b\ $ [Euclid's Lemma]

Infiniteness of non-twin primes.

Why is $1$ not a prime number?

Alternate definition of prime number

Split $n$ into nontrivial factors via a nontrivial square-root of $1\!\pmod{\!n}$

Do Arithmetic Mean and Geometric Mean of Prime Numbers converge?