Wall-Sun-Sun prime en · NOUN
Etymology
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.
Meanings
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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).
Not a single Wall-Sun-Sun prime 5lt;plt;1.6#92;times 10#123;12#125; exists [McIntosh 1995]. Carry out a search for Wall-Sun-Sun primes somewhere above this limit.
1996, Richard E. Crandall, Topics in Advanced Scientific Computation, Springer, page 113:Crandall et al. called in [56] such a prime number p satisfying p²#92;vertF#95;#123;p-(#92;fracp 5)#125; a Wall–Sun–Sun prime. There is no known example of a Wall–Sun–Sun prime and the congruence F#95;#123;p-(#92;fracp 5)#125;#92;equiv 0#92;pmod#123;p²#125;, can only be checked through explicit powering computations.
2020, Dorin Andrica, Ovidiu Bagdasar, Recurrent Sequences, Springer, page 88:Wall-Sun-Sun primes are conjectured to exist, but no example has yet been found.
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| Wall-Sun-Sun prime number | alternative | lexicographic | |
| Wall-Sun-Sun primes | Number=Plur | lexicographic |
Relateds
rank of apparition · Pisano period
Synonyms
Translations (3)
de Wall-Sun-Sun-Primzahl (conjectured prime number of a certain type) · it primo di Wall-Sun-Sun (conjectured prime number of a certain type) · fr nombre premier de Wall-Sun-Sun (conjectured prime number of a certain type)
wikipedia: Sun Zhihong · wikipedia: Sun Zhiwei · wikipedia: Donald Dines Wall