See Wall-Sun-Sun prime in All languages combined, or Wiktionary
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{
"etymology_text": "Named after American mathematician Donald Dines Wall and Chinese mathematicians Sun Zhihong and Sun Zhiwei, who have all contributed to the study of such primes.",
"forms": [
{
"form": "Wall-Sun-Sun primes",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "Wall-Sun-Sun prime (plural Wall-Sun-Sun primes)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Number theory",
"orig": "en:Number theory",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"examples": [
{
"text": "Wall-Sun-Sun primes are conjectured to exist, but no example has yet been found.",
"type": "example"
},
{
"ref": "1996, Richard E. Crandall, Topics in Advanced Scientific Computation, Springer, page 113",
"text": "Not a single Wall-Sun-Sun prime 5#x3C;p#x3C;1.6#x5C;times 10#x7B;12#x7D; exists [McIntosh 1995]. Carry out a search for Wall-Sun-Sun primes somewhere above this limit.",
"type": "quotation"
},
{
"ref": "2020, Dorin Andrica, Ovidiu Bagdasar, Recurrent Sequences, Springer, page 88",
"text": "Crandall et al. called in [56] such a prime number p satisfying p²#x5C;vertF#x5F;#x7B;p-(#x5C;fracp 5)#x7D; a Wall–Sun–Sun prime. There is no known example of a Wall–Sun–Sun prime and the congruence F#x5F;#x7B;p-(#x5C;fracp 5)#x7D;#x5C;equiv 0#x5C;pmod#x7B;p²#x7D;, can only be checked through explicit powering computations.",
"type": "quotation"
}
],
"glosses": [
"A (hypothetical) prime number p such that p² divides F_π(p), where F_n is the Fibonacci sequence and π(p) is the pth Pisano period (the period length of the Fibonacci sequence reduced modulo p)."
],
"id": "en-Wall-Sun-Sun_prime-en-noun-oZkyRqBP",
"links": [
[
"number theory",
"number theory"
],
[
"prime number",
"prime number"
],
[
"Fibonacci sequence",
"Fibonacci sequence"
],
[
"Pisano period",
"Pisano period"
],
[
"modulo",
"modulo"
]
],
"raw_glosses": [
"(number theory) A (hypothetical) prime number p such that p² divides F_π(p), where F_n is the Fibonacci sequence and π(p) is the pth Pisano period (the period length of the Fibonacci sequence reduced modulo p)."
],
"related": [
{
"word": "Pisano period"
},
{
"word": "rank of apparition"
}
],
"synonyms": [
{
"word": "Fibonacci-Wieferich prime"
},
{
"word": "Wall-Sun-Sun prime number"
}
],
"topics": [
"mathematics",
"number-theory",
"sciences"
],
"translations": [
{
"code": "fr",
"lang": "French",
"sense": "conjectured prime number of a certain type",
"tags": [
"masculine"
],
"word": "nombre premier de Wall-Sun-Sun"
},
{
"code": "de",
"lang": "German",
"sense": "conjectured prime number of a certain type",
"tags": [
"feminine"
],
"word": "Wall-Sun-Sun-Primzahl"
},
{
"code": "it",
"lang": "Italian",
"sense": "conjectured prime number of a certain type",
"tags": [
"masculine"
],
"word": "primo di Wall-Sun-Sun"
}
],
"wikipedia": [
"Donald Dines Wall",
"Sun Zhihong",
"Sun Zhiwei",
"Wall–Sun–Sun prime"
]
}
],
"word": "Wall-Sun-Sun prime"
}
{
"etymology_text": "Named after American mathematician Donald Dines Wall and Chinese mathematicians Sun Zhihong and Sun Zhiwei, who have all contributed to the study of such primes.",
"forms": [
{
"form": "Wall-Sun-Sun primes",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "Wall-Sun-Sun prime (plural Wall-Sun-Sun primes)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "Pisano period"
},
{
"word": "rank of apparition"
}
],
"senses": [
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English multiword terms",
"English nouns",
"English terms with quotations",
"English terms with usage examples",
"en:Number theory"
],
"examples": [
{
"text": "Wall-Sun-Sun primes are conjectured to exist, but no example has yet been found.",
"type": "example"
},
{
"ref": "1996, Richard E. Crandall, Topics in Advanced Scientific Computation, Springer, page 113",
"text": "Not a single Wall-Sun-Sun prime 5#x3C;p#x3C;1.6#x5C;times 10#x7B;12#x7D; exists [McIntosh 1995]. Carry out a search for Wall-Sun-Sun primes somewhere above this limit.",
"type": "quotation"
},
{
"ref": "2020, Dorin Andrica, Ovidiu Bagdasar, Recurrent Sequences, Springer, page 88",
"text": "Crandall et al. called in [56] such a prime number p satisfying p²#x5C;vertF#x5F;#x7B;p-(#x5C;fracp 5)#x7D; a Wall–Sun–Sun prime. There is no known example of a Wall–Sun–Sun prime and the congruence F#x5F;#x7B;p-(#x5C;fracp 5)#x7D;#x5C;equiv 0#x5C;pmod#x7B;p²#x7D;, can only be checked through explicit powering computations.",
"type": "quotation"
}
],
"glosses": [
"A (hypothetical) prime number p such that p² divides F_π(p), where F_n is the Fibonacci sequence and π(p) is the pth Pisano period (the period length of the Fibonacci sequence reduced modulo p)."
],
"links": [
[
"number theory",
"number theory"
],
[
"prime number",
"prime number"
],
[
"Fibonacci sequence",
"Fibonacci sequence"
],
[
"Pisano period",
"Pisano period"
],
[
"modulo",
"modulo"
]
],
"raw_glosses": [
"(number theory) A (hypothetical) prime number p such that p² divides F_π(p), where F_n is the Fibonacci sequence and π(p) is the pth Pisano period (the period length of the Fibonacci sequence reduced modulo p)."
],
"synonyms": [
{
"word": "Fibonacci-Wieferich prime"
}
],
"topics": [
"mathematics",
"number-theory",
"sciences"
],
"wikipedia": [
"Donald Dines Wall",
"Sun Zhihong",
"Sun Zhiwei",
"Wall–Sun–Sun prime"
]
}
],
"synonyms": [
{
"word": "Wall-Sun-Sun prime number"
}
],
"translations": [
{
"code": "fr",
"lang": "French",
"sense": "conjectured prime number of a certain type",
"tags": [
"masculine"
],
"word": "nombre premier de Wall-Sun-Sun"
},
{
"code": "de",
"lang": "German",
"sense": "conjectured prime number of a certain type",
"tags": [
"feminine"
],
"word": "Wall-Sun-Sun-Primzahl"
},
{
"code": "it",
"lang": "Italian",
"sense": "conjectured prime number of a certain type",
"tags": [
"masculine"
],
"word": "primo di Wall-Sun-Sun"
}
],
"word": "Wall-Sun-Sun prime"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-20 from the enwiktionary dump dated 2024-05-02 using wiktextract (1d5a7d1 and 304864d). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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