query: What is currently the biggest prime number with no smaller undiscovered prime number?
positive_passages.docid: 3007
positive_passages.text: Currently, what is the largest publicly known prime number such that all prime numbers less than it are known?
negative_passages.docid: 158213
negative_passages.text: RSA with probable primes
negative_passages.docid: 89066
negative_passages.text: Find all integers less than $m$ that are relatively prime to it
negative_passages.docid: 35096
negative_passages.text: Is the $n$-th prime smaller than $n(\log n + \log\log n-1+\frac{\log\log n}{\log n})$?
negative_passages.docid: 58114
negative_passages.text: For which primes p is $p^2 + 2$ also prime?
negative_passages.docid: 18405
negative_passages.text: What is the greatest integer that divides $p^4-1$ for every prime number $p$ greater than $5$?
negative_passages.docid: 56314
negative_passages.text: Which of the numbers $1, 2^{1/2}, 3^{1/3}, 4^{1/4}, 5^{1/5}, 6^{1/6} , 7^{1/7}$ is largest, and how to find out without calculator?
negative_passages.docid: 13739
negative_passages.text: For all $n>2$ there exists a prime number between $n$ and $ n!$
negative_passages.docid: 51305
negative_passages.text: How to verify large Mersenne Primes
negative_passages.docid: 51059
negative_passages.text: Real-world applications of prime numbers?
negative_passages.docid: 145375
negative_passages.text: RSA problem if i choose two specific small prime numbers?
negative_passages.docid: 29764
negative_passages.text: Find the largest of the three prime divisors of the number $13^4 + 16^5 - 172^2$
negative_passages.docid: 33505
negative_passages.text: Show that every large integer has a large prime-power factor
negative_passages.docid: 132132
negative_passages.text: Are there infinitely many primes of the form $6^{2n}+1$ or only finitely many?
negative_passages.docid: 83643
negative_passages.text: Are there prime gaps of every size?
negative_passages.docid: 20715
negative_passages.text: 31,331,3331, 33331,333331,3333331,33333331 are prime
negative_passages.docid: 98468
negative_passages.text: Are there infinitely many primes of the form $n!+1$?