trailThere are infinitely many pairs of primes whose difference is at most a fixed constant.
There are infinitely many pairs of primes that differ by exactly 2.
There is some N below 70 million such that infinitely many pairs of primes differ by exactly N.
Any level of distribution for primes in arithmetic progressions exceeding 1/2 implies infinitely many bounded gaps between primes.
Primes have a level of distribution exceeding 1/2 in arithmetic progressions to smooth moduli, for well-factorable weights.
There are infinitely many pairs of primes that differ by at most 246.
claim · mathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →claim page ↗︎
There are infinitely many pairs of primes whose difference is at most a fixed constant.
unassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →
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claimA box is a claim: a single proposition the graph assesses, with its own page and map. Click any claim to centre the map on it.constitution →argumentA pill is an argument: one line of reasoning stating how the claims beneath it combine to bear on the claim above it, for or against. Arguments are not destinations; click their claims to explore.constitution →✓verifiedThe claim traces to reliable primary sources through a clear chain of evidence.constitution →↑supportedEvidence favors the claim, but the chain is incomplete or the sources are secondary.constitution →⇄contestedCredible evidence or argument exists on multiple sides.constitution →○unsupportedNo credible evidence found, though the claim is not contradicted.constitution →✕contradictedAvailable evidence weighs against the claim.constitution →?unknownInsufficient information to assess.constitution →◌unassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →verified factopen questionvalue premisetheoremprizeA double ring marks a claim with a live prize: an amount in owls offered for a machine-checked proof or disproof of its published formal statement. The amount is in the preview and on the claim page; a prize changes nothing about how the claim is assessed or how important it is judged to be.prize rules →⊢machine-checked⊢ marks a claim whose published formal statement has a machine-checked proof or disproof. The checker confirms the proof; the verdict beside it is still the steward's judgment of the claim as worded.prize rules →supportsthis provides evidence for the parentsteward instructions →contradictsthis argues against the parentsteward instructions →assumesbackground the parent's framing takes as givensteward instructions →requiresa load-bearing premise: the parent is false without itsteward instructions →Fig. Detail falls off with distance; every claim is an address.