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Find a sequence of 7 consecutive primes

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#number-theory #prime-numbers
240
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Are there infinitely many quintuples of type $p, p + 2, p + 14, p + 26, p + 38$?

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#number-theory #prime-numbers
312
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Prove that $\mathbb{Q}[\sqrt{p}]$ is a field between $\mathbb{Q}$ and $\mathbb{R}$

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#field-theory #prime-numbers #extension-field #real-numbers #rational-numbers
617
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Inequality with Euler's totient function

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#prime-numbers #conjectures
278
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Find a positive integer with prime factors of at most 2, 3, 5, 7 and ends in the digits 11

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#prime-numbers #puzzle
101
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Is this "sliding window" unique?

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#number-theory #ring-theory #prime-numbers #finite-rings
575
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Relation between $(a\bmod b)\bmod c$ and $a\bmod c$

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#elementary-number-theory #discrete-mathematics #prime-numbers #modular-arithmetic
1k
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Is there any known relationship between Goldbach's comet G(n) and the prime counting function (${\pi(n)}$)?

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#number-theory #prime-numbers #goldbachs-conjecture
223
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Lemma about a prime times a unit

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#linear-algebra #ring-theory #prime-numbers
458
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this is a conjecture or a result? every arithmetic progression contains a sequence of $k$ "consecutive" primes for possibly all natural numbers $k$?

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#combinatorics #number-theory #prime-numbers #prime-gaps #arithmetic-combinatorics
70
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$x^5+a$ is reducible in $\mathbb{Z}_5[x]$ for each $a\in\mathbb{Z}_5$

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#abstract-algebra #polynomials #prime-numbers #irreducible-polynomials
3k
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Primes dividing a polynomial

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#elementary-number-theory #polynomials #prime-numbers
218
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Is there any general method of finding the lower bound of $x$ that satisfy the inequality?

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#reference-request #prime-numbers
125
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Prime Factor Problem To Solve

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#prime-numbers #prime-factorization
391
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Inequality $\varphi(N)>\pi(N)$?

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#number-theory #inequality #prime-numbers #totient-function #arithmetic-functions

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