| Proven prime cofactors of numbers of the forms 10^n + 1 and 10^n − 1 | |||
|---|---|---|---|
| From | Digits | Date | Expression (mathematically exact) |
| 10^17193 + 1 | 10355 | October 16, 2023 | 91 · (10^11462−10^5731+1) / D521,3 / D11,3 / 6573271911379053751098633975048464359927832533 |
| 10^9736 + 1 | 9665 | July 24, 2023 | (10^9736+1) / 127414554941037429648145286239939106469195284723098047037717521807235313 |
| 10^14691 + 1 | 9453 | October 13, 2023 | 91 · (10^9794−10^4897+1) / D83,3 / D59,3 / 95543233335948176474184435890844681353199716770826112802117 |
| 10^8209 − 1 | 8162 | August 14, 2023 | (10^8209−1) / 387027639720180030671334569044632439433106097191 |
| 10^5990 + 1 | 2355 | August 30, 2023 | A300 / 248484851938554257097354195919859145549341 |
| 10^7871 − 1 | 7351 | September 1, 2023 | 9 · C463,17 / (10^17−1) / 519894821582622551617789763504983559487853 |
| 10^17450 + 1 | 6929 | October 13, 2023 | B873 / 2241716371215012394459950804525216055134259097674001 |
| 10^7337 − 1 | 6125 | August 31, 2023 | (10^11−1) · C667,11 / C29,11 / C23,11 / 2459587362265548338880442635101315637 |
| 10^16150 + 1 | 5721 | September 26, 2023 | 99004980069800499001 · A808 / B48 / B43 / 2123222075537529366149482323524714527601 |
| 10^9333 + 1 | 5691 | August 31, 2023 | 999001 · (10^6222−10^3111+1) / D183,3 / D51,3 / 6044942727779144876845284825747930504069348803477678023951439948689009 |
| 10^7565 + 1 | 5579 | July 13, 2023 | 9091 · D1513,5 / D89,5 / D17,5 / 544168252889194357912197505365128821814457903492376171 |
| 10^15890 + 1 | 5397 | October 11, 2023 | A795 / B114 / 4211444349754349932180279294422518924308595774425481 |
| 10^5587 − 1 | 5333 | July 8, 2023 | 9 · C151,37 / (10^37−1) / 21812314726751445879584203746976757481394027080090123090710835090893 |
| 10^5387 − 1 | 5266 | July 16, 2023 | (10^5387−1) / 35758361120238286296955658075781822272308362560102831996163603890175134847168697546723160119470773141515244078907634316763 |
| 10^6275 − 1 | 4936 | December 9, 2023 | C1255,5 / C5,5 / 23121920617304476506542868657986769439196273737449665507828388151 |
| 10^5009 − 1 | 4933 | July 20, 2023 | (10^5009−1) / 15958226783422218436420162301509030608166735905022349421575916043441367034747 |
| 10^5726 + 1 | 4825 | December 24, 2023 | D818,7 / 547371756031537052295625700407474232103225803962681670734121759986571069341466316329 |
| 10^7503 + 1 | 4755 | August 30, 2023 | 91 · (10^5002−10^2501+1) / D61,3 / D41,3 / 928041865818872172269640654493754406088745407 |
| 10^6981 + 1 | 4230 | August 30, 2023 | 91 · (10^4654−10^2327+1) / D179,3 / D13,3 / 8577537833721208258437435856585996879133917 |
| 10^5195 + 1 | 4113 | October 8, 2023 | D1039,5 / 29790165881370054051174862609567333433578451 |
| 10^5367 + 1 | 3549 | October 8, 2023 | (10^3578−10^1789+1) / 237877908544064881785863177371 |
| 10^5139 + 1 | 3371 | December 6, 2013 | (10^3426−10^1713+1) / 31680812614988870603614117000543939651213148400456786211 |
| 10^7550 + 1 | 2943 | August 15, 2023 | B378 / 405061130479877861289812868069565059711989009708320486901776171071878363368001 |
| 10^2942 + 1 | 2885 | October 9, 2023 | (10^2942+1) / 3468561481292305322732115989794806985803274646710300721921 |
| 10^10050 + 1 | 2592 | December 16, 2023 | A503 / A168 / 92324451902583190267331881490478527886039816924248468403613097470611304150802275482188101 |
| 10^3963 + 1 | 2579 | August 29, 2023 | (10^2642−10^1321+1) / 2140678625278364922181026263981069630944358828123985539311705441 |
|
Ak = ( ( 102k−1 − 10k + 3 ) · ( 104k−2 + 102k−1 ) − 10k + 2 ) · ( 102k−1 + 1 ) − 1 Bk = ( ( 102k−1 + 10k + 3 ) · ( 104k−2 + 102k−1 ) + 10k + 2 ) · ( 102k−1 + 1 ) − 1 Ck,m = ( 10km − 1) / (10k − 1) Dk,m = ( 10km + 1) / (10k + 1) | |||
| December 25, 2023 Alfred Reich | |||