{"id":398,"date":"2026-09-27T18:19:39","date_gmt":"2026-09-27T18:19:39","guid":{"rendered":"https:\/\/mathrelated.co.uk\/?p=398"},"modified":"2026-09-30T16:56:28","modified_gmt":"2026-09-30T16:56:28","slug":"sufficiency-of-p-1-4-testing","status":"publish","type":"post","link":"https:\/\/mathrelated.co.uk\/index.php\/2026\/09\/27\/sufficiency-of-p-1-4-testing\/","title":{"rendered":"Sufficiency of (p-1)\/4 testing"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"648\" height=\"246\" src=\"https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/09\/mathsturdyChap37divided4sufficient1pseudoprimes277.jpeg\" alt=\"\" class=\"wp-image-399\" srcset=\"https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/09\/mathsturdyChap37divided4sufficient1pseudoprimes277.jpeg 648w, https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/09\/mathsturdyChap37divided4sufficient1pseudoprimes277-300x114.jpeg 300w\" sizes=\"auto, (max-width: 648px) 100vw, 648px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"632\" height=\"296\" src=\"https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/09\/mathsturdyChap37divided4sufficient2prothcompositeevidence-1.jpeg\" alt=\"\" class=\"wp-image-404\" srcset=\"https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/09\/mathsturdyChap37divided4sufficient2prothcompositeevidence-1.jpeg 632w, https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/09\/mathsturdyChap37divided4sufficient2prothcompositeevidence-1-300x141.jpeg 300w\" sizes=\"auto, (max-width: 632px) 100vw, 632px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"611\" height=\"77\" src=\"https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/09\/mathsturdyChap37divided4sufficient3conjectureZupdatedPminus1powertest.jpeg\" alt=\"\" class=\"wp-image-401\" srcset=\"https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/09\/mathsturdyChap37divided4sufficient3conjectureZupdatedPminus1powertest.jpeg 611w, https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/09\/mathsturdyChap37divided4sufficient3conjectureZupdatedPminus1powertest-300x38.jpeg 300w\" sizes=\"auto, (max-width: 611px) 100vw, 611px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">There are at least two proofs of the above conjecture now.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To disprove the above you would need to find a Proth Number of <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">the form<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"573\" height=\"53\" src=\"https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/09\/mathsturdyChap37divided4sufficient4contextZcomposite.jpeg\" alt=\"\" class=\"wp-image-402\" srcset=\"https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/09\/mathsturdyChap37divided4sufficient4contextZcomposite.jpeg 573w, https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/09\/mathsturdyChap37divided4sufficient4contextZcomposite-300x28.jpeg 300w\" sizes=\"auto, (max-width: 573px) 100vw, 573px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">This is non-trivial*<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">*No counter-examples exist for t&lt;=30,000 in our limited testing<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The following conjecture might be easier to disprove<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"643\" height=\"55\" src=\"https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/09\/mathsturdyChap37divided4sufficient5contextZnoeulerjacobipseudoprimes.jpeg\" alt=\"\" class=\"wp-image-403\" srcset=\"https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/09\/mathsturdyChap37divided4sufficient5contextZnoeulerjacobipseudoprimes.jpeg 643w, https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/09\/mathsturdyChap37divided4sufficient5contextZnoeulerjacobipseudoprimes-300x26.jpeg 300w\" sizes=\"auto, (max-width: 643px) 100vw, 643px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>There are at least two proofs of the above conjecture now. To disprove the above you would need to find a Proth Number of the form This is non-trivial* *No counter-examples exist for t&lt;=30,000 in our limited testing The following conjecture might be easier to disprove<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5,6],"tags":[14],"class_list":["post-398","post","type-post","status-publish","format-standard","hentry","category-mathematics","category-numbertheory","tag-prime"],"_links":{"self":[{"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/posts\/398","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/comments?post=398"}],"version-history":[{"count":2,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/posts\/398\/revisions"}],"predecessor-version":[{"id":424,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/posts\/398\/revisions\/424"}],"wp:attachment":[{"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/media?parent=398"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/categories?post=398"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/tags?post=398"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}