{"id":"https://openalex.org/W1983332539","doi":"https://doi.org/10.1090/s0025-5718-01-01327-8","title":"Finding prime pairs with particular gaps","display_name":"Finding prime pairs with particular gaps","publication_year":2001,"publication_date":"2001-05-11","ids":{"openalex":"https://openalex.org/W1983332539","doi":"https://doi.org/10.1090/s0025-5718-01-01327-8","mag":"1983332539"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-01-01327-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01327-8","pdf_url":"https://www.ams.org/mcom/2001-70-236/S0025-5718-01-01327-8/S0025-5718-01-01327-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2001-70-236/S0025-5718-01-01327-8/S0025-5718-01-01327-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5097531483","display_name":"Pamela Cutter","orcid":null},"institutions":[{"id":"https://openalex.org/I165733156","display_name":"University of Georgia","ror":"https://ror.org/00te3t702","country_code":"US","type":"education","lineage":["https://openalex.org/I165733156"]},{"id":"https://openalex.org/I45644089","display_name":"Albion College","ror":"https://ror.org/05nnk3913","country_code":"US","type":"education","lineage":["https://openalex.org/I45644089"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Pamela Cutter","raw_affiliation_strings":["Department of Mathematics, Albion College, Albion, Michigan 49224","Department of Mathematics, University of Georgia, Athens, Georgia 30602"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Albion College, Albion, Michigan 49224","institution_ids":["https://openalex.org/I45644089"]},{"raw_affiliation_string":"Department of Mathematics, University of Georgia, Athens, Georgia 30602","institution_ids":["https://openalex.org/I165733156"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5097531483"],"corresponding_institution_ids":["https://openalex.org/I165733156","https://openalex.org/I45644089"],"apc_list":null,"apc_paid":null,"fwci":0.6196,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.61741835,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"70","issue":"236","first_page":"1737","last_page":"1744"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9886000156402588,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6394691467285156},{"id":"https://openalex.org/keywords/annotation","display_name":"Annotation","score":0.6119822263717651},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4700058102607727},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3853760361671448}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6394691467285156},{"id":"https://openalex.org/C2776321320","wikidata":"https://www.wikidata.org/wiki/Q857525","display_name":"Annotation","level":2,"score":0.6119822263717651},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4700058102607727},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3853760361671448}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/s0025-5718-01-01327-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01327-8","pdf_url":"https://www.ams.org/mcom/2001-70-236/S0025-5718-01-01327-8/S0025-5718-01-01327-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.103.5305","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.103.5305","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2001-70-236/S0025-5718-01-01327-8/S0025-5718-01-01327-8.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.3643","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.3643","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/2001-70-236/S0025-5718-01-01327-8/S0025-5718-01-01327-8.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.48.9220","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.9220","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uga.edu/~pamelar/images/primegaps.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-01-01327-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01327-8","pdf_url":"https://www.ams.org/mcom/2001-70-236/S0025-5718-01-01327-8/S0025-5718-01-01327-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1983332539.pdf","grobid_xml":"https://content.openalex.org/works/W1983332539.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1563654733","https://openalex.org/W1965141348","https://openalex.org/W1970975159","https://openalex.org/W1992380223","https://openalex.org/W2021446977","https://openalex.org/W2068881351","https://openalex.org/W2071743058","https://openalex.org/W2079738915","https://openalex.org/W4234825099","https://openalex.org/W4252000473"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2361861616","https://openalex.org/W2263699433","https://openalex.org/W2377979023","https://openalex.org/W2218034408","https://openalex.org/W2392921965","https://openalex.org/W2358755282","https://openalex.org/W2625833328","https://openalex.org/W1533177136","https://openalex.org/W4380994516"],"abstract_inverted_index":{"By":[0,225],"a":[1,162,192,211,450],"prime":[2,121,163,193,220,230,291,340,374],"gap":[3,164,194],"of":[4,123,165,182,195,222,274,293,342,367,376,446],"size":[5,124,166,196,294,343],"<inline-formula":[6,24,37,58,80,93,125,142,167,197,237,250,295,344,379,399,421],"content-type=\"math/mathml\">":[7,25,38,59,81,94,126,143,168,198,238,251,296,345,380,400,422],"<mml:math":[8,26,39,60,82,95,127,144,169,199,239,252,297,346,381,401,423],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[9,27,40,61,83,96,128,145,170,200,240,253,298,347,382,402,424],"alttext=\"g\">":[10,129,146],"<mml:semantics>":[11,29,44,65,85,100,130,147,172,202,242,255,300,349,387,407,429],"<mml:mi>g</mml:mi>":[12,48,67,104,131,148],"<mml:annotation":[13,31,50,73,87,106,132,149,174,204,244,257,302,351,394,416,436],"encoding=\"application/x-tex\">g</mml:annotation>":[14,133,150],"</mml:semantics>":[15,33,52,75,89,108,134,151,176,206,246,259,304,353,396,418,438],"</mml:math>":[16,34,53,76,90,109,135,152,177,207,247,260,305,354,397,419,439],"</inline-formula>,":[17,208,261,398,420],"we":[18,228,266],"mean":[19],"that":[20,56,118,214],"there":[21],"are":[22,111,268],"primes":[23],"alttext=\"p\">":[28,84],"<mml:mi>p</mml:mi>":[30,46,86,102],"encoding=\"application/x-tex\">p</mml:annotation>":[32,88],"</inline-formula>":[35,54,77,91,110,136,178,248,306,355,440],"and":[36,92,262,335,441],"alttext=\"p":[41,97],"plus":[42,98,385,427],"g\">":[43,99],"<mml:mrow>":[45,66,101,388,408,430],"<mml:mo>+</mml:mo>":[47,103,391,433],"</mml:mrow>":[49,72,105,393,415,435],"encoding=\"application/x-tex\">p+g</mml:annotation>":[51,107],"such":[55,288],"the":[57,188,271,286,315,320,365,368,377],"alttext=\"g":[62],"minus":[63,405],"1\">":[64,386,406,428],"<mml:mo>\u2212<!--":[68,411],"\u2212":[69,412],"--></mml:mo>":[70,413],"<mml:mn>1</mml:mn>":[71,392,414,434],"encoding=\"application/x-tex\">g-1</mml:annotation>":[74],"numbers":[78],"between":[79],"all":[112,139,233],"composite.":[113],"It":[114],"is":[115],"widely":[116],"believed":[117],"infinitely":[119],"many":[120],"gaps":[122,221,231,292,341],"exist":[137],"for":[138,232],"even":[140,234],"integers":[141,235],"</inline-formula>.":[153],"However,":[154],"it":[155],"had":[156],"not":[157,269],"previously":[158],"been":[159],"known":[160],"whether":[161],"alttext=\"1000\">":[171,201,254,299,348],"<mml:mn>1000</mml:mn>":[173,203,256,301,350],"encoding=\"application/x-tex\">1000</mml:annotation>":[175,205,258,303,352],"existed.":[179],"The":[180,290],"objective":[181],"this":[183,226,309],"article":[184,310],"was":[185],"to":[186,190,218,249,319,372,444],"be":[187,454],"first":[189,272,287,312],"find":[191,229,267,373],"by":[209,449],"using":[210,359],"systematic":[212],"method":[213],"would":[215],"also":[216,453],"apply":[217],"finding":[219],"any":[223],"size.":[224],"method,":[227],"from":[236],"alttext=\"746\">":[241],"<mml:mn>746</mml:mn>":[243],"encoding=\"application/x-tex\">746</mml:annotation>":[245],"some":[263],"beyond.":[264],"What":[265],"necessarily":[270],"occurrences":[273],"these":[275],"gaps,":[276],"but,":[277],"being":[278],"examples,":[279],"they":[280],"give":[281],"an":[282],"upper":[283],"bound":[284],"on":[285,314,324],"occurrences.":[289],"listed":[307],"in":[308],"were":[311],"announced":[313],"Number":[316],"Theory":[317],"Listing":[318],"World":[321],"Wide":[322],"Web":[323],"Tuesday,":[325],"April":[326],"8,":[327],"1997.":[328],"Since":[329],"then,":[330],"others,":[331],"including":[332],"Sol":[333],"Weintraub":[334],"A.O.L.":[336],"Atkin,":[337],"have":[338],"found":[339],"with":[356],"smaller":[357],"integers,":[358],"more":[360],"ad":[361],"hoc":[362],"methods.":[363],"At":[364],"end":[366],"article,":[369],"related":[370],"computations":[371],"triples":[375],"form":[378],"alttext=\"6":[383],"m":[384,404,426],"<mml:mn>6</mml:mn>":[389],"<mml:mi>m</mml:mi>":[390,410,432],"encoding=\"application/x-tex\">6m+1</mml:annotation>":[395],"alttext=\"12":[403,425],"<mml:mn>12</mml:mn>":[409,431],"encoding=\"application/x-tex\">12m-1</mml:annotation>":[417],"encoding=\"application/x-tex\">12m+1</mml:annotation>":[437],"their":[442],"application":[443],"divisibility":[445],"binomial":[447],"coefficients":[448],"square":[451],"will":[452],"discussed.":[455]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
