Erdős problem 1074 · problems.science

Similarly, if $P$ is the set of all primes $p$ such that there exists an $m$ with $p\not\equiv 1\pmod{m}$ such that $m! + 1 \equiv 0\pmod{p}$ , then does $\lim\frac{|P\cap[1, x]|}{\pi(x)}$ exist?

Sources

Browse retained paths and inspect the exact material available for this Problem.

12 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

1074.lean

Retained formal statement8 of 12

Pillai [Pi30] raised the question of whether there exist any primes in $P$ . This was answered by Chowla, who noted that, for example, $14! + 1 \equiv 18! + 1 \equiv 0 \pmod{23}$ .

FormalConjectures/ErdosProblems/1074.leanErdos1074.erdos_1074.variants.mem_pillaiPrimes1 lineExact file

123 ∈ Erdos1074.PillaiPrimes

TestStatement only, no proof

Sources

Search problems.science