The board / number theory / #854
Erdős Problem #854
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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Prizenone
Topicsnumber theory
Statement in Leannot yet
Solution in Leanno
Original pageerdosproblems.com/854
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Proved (modulo PNT and Mertens) liminf F(k)/(k log log k) >= e^gamma and Q(k) >= (e^gamma/2-o(1))k log log k; independently verified exact F(k) through k=13, full gap sets through k=8, and F(100)>=482
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