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- Home_prime abstract "In number theory, the home prime HP(n) of an integer n greater than 1 is the prime obtained by repeatedly factoring the increasing concatenation of prime factors including repetitions. The mth intermediate stage in the process of determining HP(n) is designated HPn(m). For instance, HP(10) = 773, as 10 factors as 2×5 yielding HP10(1) = 25, 25 factors as 5×5 yielding HP10(2) = HP25(1) = 55, 55 = 5×11 implies HP10(3) = HP25(2) = HP55(1) = 511, and 511 = 7×73 gives HP10(4) = HP25(3) = HP55(2) = HP511(1) = 773, a prime number. Some sources use the alternative notation HPn for the homeprime, leaving out parentheses. Investigations into home primes make up a minor side issue in number theory. Its questions have served as test fields for the implementation of efficient algorithms for factoring composite numbers, but the subject is really one in recreational mathematics.The outstanding computational problem as of 2012 is whether HP(49) = HP(77) can be calculated in practice. As each iteration is greater than the previous up until a prime is reached, factorizations generally grow more difficult so long as an end is not reached. As of September 2012 the pursuit of HP(49) concerns the factorization of a 210-digit composite factor of HP49(117) after a break was achieved on 8 September 2012 with the calculation of HP49(110). This followed a stretch extending for the larger part of a decade that made extensive use of computational resources, with the successful factorization of a 178-digit composite in HP49(104) into 88- and 90-digit primes on 11 January 2011. Details of the history of this search, as well as the sequences leading to home primes for all other numbers through 100, are maintained at Patrick De Geest's worldofnumbers website. A wiki primarily associated with the Great Internet Mersenne Prime Search maintains the complete known data through 1000 in base 10 and also has lists for the bases 2 through 9.The primes in HP(n) are1, 2, 3, 211, 5, 23, 7, 3331113965338635107, 311, 773, 11, 223, 13, 13367, 1129, 31636373, 17, 233, 19, 3318308475676071413, 37, 211, 23, 331319, 773, 3251, 13367, 227, 29, 547, ... (sequence A037274 in OEIS)Aside from the computational problems that have had so much time devoted to them, it appears absolute proof of existence of a home prime for any specific number might entail its effective computation. In purely heuristic terms, the existence has probability 1 for all numbers, but such heuristics make assumptions about numbers drawn from a wide variety of processes that, though they likely are correct, fall short of the standard of proof usually required of mathematical claims.".
- Home_prime wikiPageExternalLink HomePrime.html.
- Home_prime wikiPageExternalLink A037274.
- Home_prime wikiPageExternalLink Home_Primes_Search.
- Home_prime wikiPageExternalLink topic1.htm.
- Home_prime wikiPageID "30033327".
- Home_prime wikiPageLength "5667".
- Home_prime wikiPageOutDegree "29".
- Home_prime wikiPageRevisionID "623875173".
- Home_prime wikiPageWikiLink Algorithm.
- Home_prime wikiPageWikiLink Base_10.
- Home_prime wikiPageWikiLink Category:Base-dependent_integer_sequences.
- Home_prime wikiPageWikiLink Category:Integer_sequences.
- Home_prime wikiPageWikiLink Category:Recreational_mathematics.
- Home_prime wikiPageWikiLink Composite_number.
- Home_prime wikiPageWikiLink Concatenation_(mathematics).
- Home_prime wikiPageWikiLink Decimal.
- Home_prime wikiPageWikiLink Existence.
- Home_prime wikiPageWikiLink Great_Internet_Mersenne_Prime_Search.
- Home_prime wikiPageWikiLink Heuristic.
- Home_prime wikiPageWikiLink Integer.
- Home_prime wikiPageWikiLink Integer_factorization.
- Home_prime wikiPageWikiLink Journal_of_Recreational_Mathematics.
- Home_prime wikiPageWikiLink List_of_recreational_number_theory_topics.
- Home_prime wikiPageWikiLink Mathematical_proof.
- Home_prime wikiPageWikiLink Number_theory.
- Home_prime wikiPageWikiLink OEIS.
- Home_prime wikiPageWikiLink On-Line_Encyclopedia_of_Integer_Sequences.
- Home_prime wikiPageWikiLink Patrick_De_Geest.
- Home_prime wikiPageWikiLink Persistence_of_a_number.
- Home_prime wikiPageWikiLink Prime_factor.
- Home_prime wikiPageWikiLink Prime_factorization.
- Home_prime wikiPageWikiLink Prime_number.
- Home_prime wikiPageWikiLink Recreational_mathematics.
- Home_prime wikiPageWikiLink Wiki.
- Home_prime wikiPageWikiLink Worldofnumbers.
- Home_prime wikiPageWikiLinkText "Home prime".
- Home_prime wikiPageWikiLinkText "home prime".
- Home_prime hasPhotoCollection Home_prime.
- Home_prime wikiPageUsesTemplate Template:As_of.
- Home_prime wikiPageUsesTemplate Template:OEIS.
- Home_prime subject Category:Base-dependent_integer_sequences.
- Home_prime subject Category:Integer_sequences.
- Home_prime subject Category:Recreational_mathematics.
- Home_prime type Article.
- Home_prime type Article.
- Home_prime type Combinatoric.
- Home_prime type Field.
- Home_prime type Integer.
- Home_prime comment "In number theory, the home prime HP(n) of an integer n greater than 1 is the prime obtained by repeatedly factoring the increasing concatenation of prime factors including repetitions. The mth intermediate stage in the process of determining HP(n) is designated HPn(m).".
- Home_prime label "Home prime".
- Home_prime sameAs m.0g54y2k.
- Home_prime sameAs Q5889155.
- Home_prime sameAs Q5889155.
- Home_prime wasDerivedFrom Home_prime?oldid=623875173.
- Home_prime isPrimaryTopicOf Home_prime.