query: what is the greatest integer that divides $p^4-1$ for every prime number p greater than 5
positive_passages.docid: 18405
positive_passages.text: What is the greatest integer that divides $p^4-1$ for every prime number $p$ greater than $5$?
negative_passages.docid: 68376
negative_passages.text: How, if at all, does pure mathematics benefit from $2^{74207281}-1$ being prime?
negative_passages.docid: 100255
negative_passages.text: If a prime divides the hypotenuse of a primitive Pythagorean triple, then $p \equiv 1$ (mod 4)
negative_passages.docid: 54547
negative_passages.text: Prove this number must be a prime number or 1.
negative_passages.docid: 63710
negative_passages.text: For x < 5 what is the greatest value of x
negative_passages.docid: 15915
negative_passages.text: For any prime $p > 3$, why is $p^2-1$ always divisible by 24?
negative_passages.docid: 44857
negative_passages.text: Why the $(n+1)$th prime number cannot exceed the smallest prime divisor of $p_1\dotsc p_n + 1$
negative_passages.docid: 131488
negative_passages.text: Show that $p^3+4$ is prime
negative_passages.docid: 126945
negative_passages.text: checking if a number is a prime
negative_passages.docid: 12250
negative_passages.text: How to find the prime factorization of $100!$.
negative_passages.docid: 148217
negative_passages.text: A polynomial with integer coefficients that attains the value $5$ at four distinct points
negative_passages.docid: 119486
negative_passages.text: Upper and Lower bounds on the nth prime number
negative_passages.docid: 70066
negative_passages.text: Show that product of primes, $\prod_{k=1}^{\pi(n)} p_k < 4^n$
negative_passages.docid: 157884
negative_passages.text: For any prime $p>3$ show that 3 divides $2p^2+1$
negative_passages.docid: 98468
negative_passages.text: Are there infinitely many primes of the form $n!+1$?
negative_passages.docid: 50781
negative_passages.text: $(n+1)$th prime $p_{n+1}$ less than or equal to $p_1p_2\dots p_n+1$
negative_passages.docid: 68688
negative_passages.text: n-th prime number is less than $4^n$