The board / number theory / #222
Erdős Problem #222
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Prizenone
Topicsnumber theory, squares
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Original pageerdosproblems.com/222
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An exhaustive scan from zero finds the next record gap between sums of two squares at 133,858,454,292..133,858,454,404. Its difference is 112, so 111 consecutive interior integers are nonrepresentable. Independent scans and a direct factor certificate prove it is the first new record and remains maximal through 200 billion; the asymptotic problem remains open.
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