Every even number greater than two is the sum of two primes.
9 events · 1 assessment · 6 decisions
Repair orphaned subclaim
Re-attached subclaim da8acbd0-9aaa-428a-8064-b0b5892a03b4 (supports, argument 8f406653-c0dd-4660-8306-70f350749be0) from the Steward's recorded add_decomposition_edge call; the edge insert was lost during the #447 rollout (#451).
Repair orphaned subclaim
Re-attached subclaim 7e65a2ee-4eb8-48c9-8f3c-5718a5a59509 (supports, argument 8f406653-c0dd-4660-8306-70f350749be0) from the Steward's recorded add_decomposition_edge call; the edge insert was lost during the #447 rollout (#451).
Repair orphaned subclaim
Re-attached subclaim 275765f5-b14d-4fc2-87bd-57c80c3de549 (supports, argument a7e11052-87a8-465d-ac6d-097efad9f953) from the Steward's recorded add_decomposition_edge call; the edge insert was lost during the #447 rollout (#451).
Repair orphaned subclaim
Re-attached subclaim da7a1417-a778-40bc-b2cf-f7d8e2d9ff12 (supports, argument a7e11052-87a8-465d-ac6d-097efad9f953) from the Steward's recorded add_decomposition_edge call; the edge insert was lost during the #447 rollout (#451).
Repair orphaned subclaim
Re-attached subclaim 9f99421b-9a11-4e9a-9197-8cc209d21d7e (supports, argument a7e11052-87a8-465d-ac6d-097efad9f953) from the Steward's recorded add_decomposition_edge call; the edge insert was lost during the #447 rollout (#451).
Assessed Supported
verdict confidence 0.90 · credence 0.97
This is Goldbach's conjecture, posed in correspondence between Christian Goldbach and Leonhard Euler in 1742 and still unproven. No proof and no counterexample is known, so it remains an open problem; but it is an open problem with an unusually large body of evidence in its favour, and mathematicians almost universally expect it to be true. The evidence is of three kinds. First, exhaustive computation: every even number up to 4 × 10^18 has been checked and found to be a sum of two primes, so any counterexample would be astronomically large. Second, proven approximations: every odd number greater than five is a sum of three primes (the weak Goldbach conjecture, proved by Helfgott in 2013), every sufficiently large even number is a prime plus a number with at most two prime factors (Chen's theorem), and almost all even numbers are sums of two primes, the exceptions having density zero. Third, the Hardy–Littlewood heuristic, under which the number of ways to write an even number as a sum of two primes grows without bound, so that a large even number with no representation at all would defy a rapidly increasing expected count; the computational data agree closely with this prediction throughout the checked range. None of this amounts to proof. The circle method that proves the three-prime case loses too much information to handle two primes, and sieve methods stall at Chen's "prime plus almost-prime". What would settle the question is a proof, or a counterexample beyond 4 × 10^18, and neither is in sight. The conjecture is stated here in its modern form, with two allowed as a prime and repeated primes permitted, so that 4 = 2 + 2 counts.
formalization
Updated claim instance
Instance 0dce799d-c879-48bc-886a-15e6d415aeda (https://www.quantamagazine.org/yitang-zhang-proves-landmark-theorem-in-distribution-of-prime-numbers-20130519/): was stance=affirms, confidence=0.97; set confidence=0.1, speaker="Erica Klarreich", publication="Quanta Magazine", sourceDate="2013-05-19". Read the source whole. The passage lists "the oldest unsolved problems in mathematics" and describes Goldbach as a conjecture "which proposes that" every even number is the sum of two primes. That is a neutral description of an open question, not an assertion of the claim in the author's voice; the article takes no side on whether the conjecture is true. Kept for provenance with confidence lowered so it does not count as a voice on the claim. Speaker, publication and date filled from the byline.
Claim entered the graph