About: Proth prime

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A Proth number is a natural number N of the form where k and n are positive integers, k is odd and . A Proth prime is a Proth number that is prime. They are named after the French mathematician François Proth. The first few Proth primes are 3, 5, 13, 17, 41, 97, 113, 193, 241, 257, 353, 449, 577, 641, 673, 769, 929, 1153, 1217, 1409, 1601, 2113, 2689, 2753, 3137, 3329, 3457, 4481, 4993, 6529, 7297, 7681, 7937, 9473, 9601, 9857 (OEIS: ). The primality of Proth numbers can be tested more easily than many other numbers of similar magnitude.

Attributes	Values
rdf:type	Thing
rdfs:label	Proth prime (en)
rdfs:comment	A Proth number is a natural number N of the form where k and n are positive integers, k is odd and . A Proth prime is a Proth number that is prime. They are named after the French mathematician François Proth. The first few Proth primes are 3, 5, 13, 17, 41, 97, 113, 193, 241, 257, 353, 449, 577, 641, 673, 769, 929, 1153, 1217, 1409, 1601, 2113, 2689, 2753, 3137, 3329, 3457, 4481, 4993, 6529, 7297, 7681, 7937, 9473, 9601, 9857 (OEIS: ). The primality of Proth numbers can be tested more easily than many other numbers of similar magnitude. (en)
rdfs:seeAlso	Proth's theorem
dcterms:subject	Classes of prime numbers
Wikipage page ID	62508931 (xsd:integer)
Wikipage revision ID	1110791793 (xsd:integer)
Link from a Wikipage to another Wikipage	PrimeGrid Prime numbers Cullen number Deterministic algorithm Proth's theorem Probable prime Conjecture Sierpinski number Composite number François Proth Parity (mathematics) Las Vegas algorithm Fermat number Classes of prime numbers Discrete logarithm False positives and false negatives Goldbach's weak conjecture Harald Helfgott Prime number Binary number Thabit number Diffie–Hellman problem Integer Mersenne prime Microsoft Natural number Seventeen or Bust Soft O Generalized Fermat number dbr:Den_Boer_reduction dbr:Volunteer_computing_project
sameAs	Proth prime Proth prime
terms number	4304683178 (xsd:decimal)
dbp:wikiPageUsesTemplate	dbt:As_of dbt:Better_source dbt:Cn dbt:Reflist dbt:See_also dbt:Short_description dbt:OEIS2C dbt:Prime_number_classes dbt:Infobox_integer_sequence
author	Proth, Francois (en)
named after	François Proth
has abstract	A Proth number is a natural number N of the form where k and n are positive integers, k is odd and . A Proth prime is a Proth number that is prime. They are named after the French mathematician François Proth. The first few Proth primes are 3, 5, 13, 17, 41, 97, 113, 193, 241, 257, 353, 449, 577, 641, 673, 769, 929, 1153, 1217, 1409, 1601, 2113, 2689, 2753, 3137, 3329, 3457, 4481, 4993, 6529, 7297, 7681, 7937, 9473, 9601, 9857 (OEIS: ). It is still an open question whether an infinite number of Proth primes exist. It was shown in 2022 that the reciprocal sum of Proth primes converges to a real number near 0.747392479, substantially less than the value of 1.093322456 for the reciprocal sum of Proth numbers. The primality of Proth numbers can be tested more easily than many other numbers of similar magnitude. (en)
con number	Infinite (en)
first terms	3513174197113 (xsd:decimal)
formula	k × 2n + 1 (en)
largest known term	10223 (xsd:integer)
OEIS	A080076 (en)
OEIS name	Proth primes: primes of the form k*2^m + 1 with odd k < 2^m, m ≥ 1 (en)
parentsequence	Proth numbers, prime numbers (en)
publication year	1878 (xsd:integer)
prov:wasDerivedFrom	wikipedia-en:Proth_prime?oldid=1110791793&ns=0
page length (characters) of wiki page	14371 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Proth_prime
is Link from a Wikipage to another Wikipage of	PrimeGrid Proth primes 1,000,000,000 10,000 1000 (number) 113 (number) François Proth Proth number 500 (number) 700 (number) 900 (number) 97 (number) Largest known prime number 241 (number) 600 (number) 9000 (number) 3000 (number) 300 (number) 400 (number) 41 (number) 2000 (number) Prime number Pierpont prime Mersenne prime Orders of magnitude (numbers) List of volunteer computing projects Proth numbers
is Wikipage redirect of	Proth primes Proth number Proth numbers
is foaf:primaryTopic of	wikipedia-en:Proth_prime

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