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 →quantityA box with a rule beneath its text is a quantity: a value the graph estimates rather than a proposition it affirms or denies. Its estimate stands where a claim's status would.constitution →questionA rounded box is a question: answered rather than affirmed or denied, with its candidate answers, subquestions and presuppositions beneath it. Its mark says how well answered it is.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. Click one to see its reasoning and open its page.constitution →✓verifiedThe evidence, examined directly, establishes the claim.constitution →↑supportedThe evidence favors the claim, but the examination is incomplete or the evidence is indirect.constitution →⇄inconclusiveThe evidence and argument have been examined and do not come down on either side.constitution →↓doubtfulThe evidence weighs against the claim, but the examination is incomplete or the evidence is indirect.constitution →✕contradictedThe evidence, examined directly, 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 factunsettledvalue 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 →answersa candidate answer to the questionconstitution →Fig. Detail falls off with distance; every claim is an address.