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problems.yaml
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13398 lines (12187 loc) · 248 KB
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- number: "1"
prize: "$500"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["A276661"]
formalized:
state: "yes"
last_update: "2025-08-31"
tags: ["number theory", "additive combinatorics"]
- number: "2"
prize: "$1000"
status:
state: "disproved"
last_update: "2025-08-31"
formalized:
state: "no"
last_update: "2025-08-31"
oeis: ["A160559"]
tags: ["number theory", "covering systems"]
- number: "3"
prize: "$5000"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["A003002", "A003003", "A003004", "A003005"]
formalized:
state: "yes"
last_update: "2025-08-31"
tags: ["number theory", "additive combinatorics", "arithmetic progressions"]
- number: "4"
prize: "$10000"
status:
state: "proved"
last_update: "2025-08-31"
tags: ["number theory", "primes"]
oeis: ["A002386"]
formalized:
state: "yes"
last_update: "2025-08-31"
- number: "5"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["A001223"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["number theory", "primes"]
- number: "6"
prize: "$100"
status:
state: "proved"
last_update: "2025-08-31"
oeis: ["A335277"]
formalized:
state: "yes"
last_update: "2025-09-18"
tags: ["number theory", "primes"]
- number: "7"
prize: "no"
status:
state: "verifiable"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["number theory", "covering systems"]
- number: "8"
prize: "no"
status:
state: "disproved"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["number theory", "covering systems"]
- number: "9"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["A006286"]
formalized:
state: "yes"
last_update: "2025-08-31"
tags: ["number theory", "additive basis", "primes"]
- number: "10"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["A387053"]
formalized:
state: "yes"
last_update: "2025-08-31"
tags: ["number theory", "additive basis", "primes"]
- number: "11"
prize: "no"
status:
state: "open"
last_update: "2026-03-14"
oeis: ["A001220", "A377587"]
formalized:
state: "yes"
last_update: "2025-08-31"
tags: ["number theory", "additive basis"]
- number: "12"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "yes"
last_update: "2025-08-31"
tags: ["number theory"]
- number: "13"
prize: "$100"
status:
state: "proved"
last_update: "2025-08-31"
oeis: ["A002264"]
formalized:
state: "yes"
last_update: "2026-02-02"
tags: ["number theory"]
- number: "14"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["A143824", "possible"]
formalized:
state: "yes"
last_update: "2025-11-02"
tags: ["number theory", "sidon sets", "additive combinatorics"]
- number: "15"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["number theory", "primes"]
- number: "16"
prize: "no"
status:
state: "disproved (Lean)"
last_update: "2026-02-24"
oeis: ["A006285"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["number theory", "additive basis", "primes"]
- number: "17"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["A038133"]
formalized:
state: "yes"
last_update: "2025-08-31"
comments: "cluster primes"
tags: ["number theory", "primes"]
- number: "18"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["A005153"]
formalized:
state: "yes"
last_update: "2026-03-15"
comments: "practical numbers"
tags: ["number theory", "divisors", "factorials"]
- number: "19"
prize: "$500"
status:
state: "decidable"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory", "chromatic number"]
- number: "20"
prize: "$1000"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["A332077"]
formalized:
state: "yes"
last_update: "2025-08-31"
comments: "sunflower conjecture"
tags: ["combinatorics"]
- number: "21"
prize: "$500"
status:
state: "proved"
last_update: "2025-08-31"
oeis: ["A391599"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["combinatorics", "intersecting family"]
- number: "22"
prize: "no"
status:
state: "proved"
last_update: "2025-08-31"
oeis: ["possible"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory"]
- number: "23"
prize: "no"
status:
state: "falsifiable"
last_update: "2025-08-31"
oeis: ["A389646"]
formalized:
state: "yes"
last_update: "2026-02-17"
tags: ["graph theory"]
- number: "24"
prize: "no"
status:
state: "proved"
last_update: "2025-08-31"
oeis: ["possible"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory"]
- number: "25"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "yes"
last_update: "2025-12-28"
tags: ["number theory"]
- number: "26"
prize: "no"
status:
state: "disproved (Lean)"
last_update: "2025-12-28"
oeis: ["N/A"]
formalized:
state: "yes"
last_update: "2025-11-25"
tags: ["number theory", "divisors"]
- number: "27"
prize: "$100"
status:
state: "disproved"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["number theory", "covering systems"]
- number: "28"
prize: "$500"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "yes"
last_update: "2025-08-31"
tags: ["number theory", "additive basis"]
- number: "29"
prize: "$100"
status:
state: "proved"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["number theory", "additive basis"]
- number: "30"
prize: "$1000"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["A143824", "A227590", "A003022"]
formalized:
state: "yes"
last_update: "2025-08-31"
tags: ["number theory", "sidon sets", "additive combinatorics"]
- number: "31"
prize: "no"
status:
state: "proved (Lean)"
last_update: "2025-11-24"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["number theory", "additive basis"]
- number: "32"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "yes"
last_update: "2026-02-13"
tags: ["number theory", "additive basis"]
- number: "33"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "yes"
last_update: "2025-09-04"
tags: ["number theory", "additive basis"]
- number: "34"
prize: "no"
status:
state: "disproved (Lean)"
last_update: "2026-02-05"
oeis: ["A389241", "A234813", "A390187"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["number theory"]
- number: "35"
prize: "no"
status:
state: "proved"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["number theory", "additive basis"]
- number: "36"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["A393584", "possible"]
formalized:
state: "yes"
last_update: "2025-08-31"
comments: "minimum overlap problem"
tags: ["number theory", "additive combinatorics"]
- number: "37"
prize: "no"
status:
state: "disproved"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["number theory", "additive combinatorics"]
- number: "38"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "yes"
last_update: "2025-12-20"
tags: ["number theory"]
- number: "39"
prize: "$500"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "yes"
last_update: "2025-08-31"
tags: ["number theory", "sidon sets", "additive combinatorics"]
- number: "40"
prize: "$500"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "yes"
last_update: "2025-08-31"
tags: ["number theory", "additive basis"]
- number: "41"
prize: "$500"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "yes"
last_update: "2025-08-31"
tags: ["number theory", "sidon sets", "additive combinatorics"]
- number: "42"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "yes"
last_update: "2025-10-20"
tags: ["number theory", "sidon sets", "additive combinatorics"]
- number: "43"
prize: "$100"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["A143824", "A227590", "A003022", "possible"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["number theory", "sidon sets", "additive combinatorics"]
- number: "44"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "yes"
last_update: "2025-08-31"
tags: ["number theory", "sidon sets", "additive combinatorics"]
- number: "45"
prize: "no"
status:
state: "proved"
last_update: "2025-08-31"
oeis: ["possible"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["number theory", "unit fractions", "ramsey theory"]
- number: "46"
prize: "no"
status:
state: "proved (Lean)"
last_update: "2025-12-29"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["number theory", "unit fractions", "ramsey theory"]
- number: "47"
prize: "$100"
status:
state: "proved (Lean)"
last_update: "2025-11-28"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-12-02"
tags: ["number theory", "unit fractions"]
- number: "48"
prize: "no"
status:
state: "proved"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "yes"
last_update: "2025-08-31"
tags: ["number theory"]
- number: "49"
prize: "no"
status:
state: "proved"
last_update: "2025-08-31"
oeis: ["A365339", "A365474"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["number theory", "primes"]
- number: "50"
prize: "$250"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "yes"
last_update: "2026-03-19"
tags: ["number theory"]
- number: "51"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["A002202", "A014197"]
formalized:
state: "yes"
last_update: "2025-09-25"
tags: ["number theory"]
- number: "52"
prize: "$250"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["A263996"]
formalized:
state: "no"
last_update: "2025-08-31"
comments: "sum-product problem"
tags: ["number theory", "additive combinatorics"]
- number: "53"
prize: "no"
status:
state: "proved"
last_update: "2025-08-31"
oeis: ["possible"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["number theory", "additive combinatorics"]
- number: "54"
prize: "$100"
status:
state: "solved"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["number theory", "ramsey theory"]
- number: "55"
prize: "$250"
status:
state: "solved"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["number theory", "ramsey theory"]
- number: "56"
prize: "$10"
status:
state: "disproved (Lean)"
last_update: "2025-11-26"
oeis: ["N/A"]
formalized:
state: "yes"
last_update: "2025-08-31"
tags: ["number theory", "intersecting family"]
- number: "57"
prize: "no"
status:
state: "proved"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory", "chromatic number", "cycles"]
- number: "58"
prize: "no"
status:
state: "proved"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory", "chromatic number", "cycles"]
- number: "59"
prize: "no"
status:
state: "disproved"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory", "turan number"]
- number: "60"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["possible"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory", "cycles"]
- number: "61"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "yes"
last_update: "2025-09-30"
tags: ["graph theory"]
- number: "62"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory"]
- number: "63"
prize: "no"
status:
state: "proved"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory", "chromatic number", "cycles"]
- number: "64"
prize: "$1000"
status:
state: "falsifiable"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "yes"
last_update: "2025-08-31"
tags: ["graph theory", "cycles"]
- number: "65"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory", "cycles"]
- number: "66"
prize: "$500"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "yes"
last_update: "2025-08-31"
tags: ["number theory", "additive basis"]
- number: "67"
prize: "$500"
status:
state: "proved"
last_update: "2025-08-31"
oeis: ["A181740", "A237695"]
formalized:
state: "yes"
last_update: "2025-11-04"
comments: "Erdős discrepancy problem"
tags: ["discrepancy"]
- number: "68"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["A331373"]
formalized:
state: "yes"
last_update: "2025-08-31"
tags: ["number theory", "irrationality"]
- number: "69"
prize: "no"
status:
state: "proved"
last_update: "2025-12-2"
oeis: ["A262153"]
formalized:
state: "yes"
last_update: "2025-08-31"
tags: ["number theory", "irrationality"]
- number: "70"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory", "ramsey theory", "set theory"]
- number: "71"
prize: "no"
status:
state: "proved"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory", "cycles"]
- number: "72"
prize: "$100"
status:
state: "proved"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory", "cycles"]
- number: "73"
prize: "no"
status:
state: "proved"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory"]
- number: "74"
prize: "$500"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "yes"
last_update: "2025-09-25"
tags: ["graph theory", "chromatic number", "cycles"]
- number: "75"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "yes"
last_update: "2026-04-04"
tags: ["graph theory", "chromatic number"]
- number: "76"
prize: "no"
status:
state: "proved"
last_update: "2025-08-31"
oeis: ["A060407"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory", "ramsey theory"]
- number: "77"
prize: "$250"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["A059442"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory", "ramsey theory"]
- number: "78"
prize: "$100"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["A059442"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory", "ramsey theory"]
- number: "79"
prize: "no"
status:
state: "proved"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory", "ramsey theory"]
- number: "80"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory", "ramsey theory"]
- number: "81"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["possible"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory"]
- number: "82"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["A120414", "A390256", "A390257", "A390919", "A392636",
"A394400", "A394462", "A394539", "A394563", "A394564",
"A394573", "A394574", "A394930", "A394933"]
formalized:
state: "yes"
last_update: "2026-01-17"
tags: ["graph theory"]
- number: "83"
prize: "$500"
status:
state: "proved"
last_update: "2025-08-31"
oeis: ["A071799", "A387635"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["combinatorics"]
- number: "84"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["possible"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory", "cycles"]
- number: "85"
prize: "no"
status:
state: "open"
last_update: "2026-03-14"
oeis: ["A006672", "possible"]
formalized:
state: "yes"
last_update: "2025-11-21"
tags: ["graph theory"]
- number: "86"
prize: "$100"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["A245762"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory"]
- number: "87"
prize: "no"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["A059442", "possible"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory", "ramsey theory"]
- number: "88"
prize: "$100"
status:
state: "proved"
last_update: "2025-08-31"
oeis: ["N/A"]
formalized:
state: "no"
last_update: "2025-08-31"
tags: ["graph theory", "ramsey theory"]
- number: "89"
prize: "$500"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["A186704", "A131628"]
formalized:
state: "yes"
last_update: "2025-10-24"
comments: "Erdős distance problem"
tags: ["geometry", "distances"]
- number: "90"
prize: "$500"
status:
state: "open"
last_update: "2025-08-31"
oeis: ["A186705"]
formalized:
state: "yes"
last_update: "2025-09-25"
comments: "unit distance problem"
tags: ["geometry", "distances"]