Visa källa för Lista över primtal

{{Ofullständig lista}}
{{Flera bilder|perrow=2|total_width=400
| image1 = Primencomposite0100.svg
| image2 = PDensity.JPG
| image3 = Primes3D.gif
| image4 = A 150x150 Ulam spiral of dots with varying widths.svg
| footer = Medurs från övre vänstra bilden: [[De naturliga talen]] från 0 till 100 där primtalen är i <span style="color: #ff0000;">rött</span>, de sammansatta talen är i <span style="color: #7fff00;">grönt</span> samt [[0 (tal)|0]] och [[1 (tal)|1]] är i <span style="color: #ffffff;">vitt</span>. En [[graf]] över det totala antalet primtal som följer varandra mellan [[Kvadrattal|kvadrattalen]] mot [[Kvadratrot|kvadratroten]] på det nedre kvadrattalet. [[Ulams spiral]] av storleken 150x150 prickar med varierande storlek på prickarna. Animering över fördelningen av primtalen i tre dimensioner.}}

Detta är en '''lista över primtal''' som ordnas [[Ordinaltal|ordinalt]] men även efter [[Lista över primtalsklasser|olika klasser av primtal]]. Ett [[primtal]] är ett [[naturligt tal]], som är större än [[1 (tal)|1]] och som inte har några andra positiva [[Delbarhet|delare]] än 1 och talet självt.<ref>{{Bokref|titel=The Mathematical Olympiad Handbook: An Introduction to Problem Solving Based on the First 32 British Mathematical Olympiads 1965–1996|url=https://archive.org/details/mathematicalolym1997gard/page/26|utgivare=[[Oxford University Press]]|datum=1997|hämtdatum=13 augusti 2020|isbn=0-19-850105-6|oclc=37024771|efternamn=Gardiner|förnamn=Tony|sid=26|författarlänk=Tony Gardiner|språk=engelska|libris=4628496|utgivningsort=New York}}</ref> Enligt [[Euklides sats]] finns det oändligt många primtal.<ref>{{Bokref|titel=Number Theory and Its History.|url=https://books.google.se/books?id=Sl_6BPp7S0AC&printsec=frontcover&hl=sv&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false|utgivare=[[Dover Publications]]|hämtdatum=13 augusti 2020|isbn=0-486-65620-9|oclc=868561429|efternamn=Ore|förnamn=Øystein|år=1988|sid=65|origår=1948|språk=engelska|utgivningsort=New York|libris=4993438|upplaga=2|författarlänk=Øystein Ore}}</ref> De första {{Nowrap|1 000}} primtalen visas i den första tabellen, följt av listor med anmärkningsvärda typer av primtal i alfabetisk ordning. Notera att 1 varken är ett primtal eller ett [[sammansatt tal]].{{Anmärkning|1 är varken ett primtal eller ett sammansatt tal enligt konvention, utan kategoriseras som en [[Enhet (ringteori)|enhet]]. Vid första anblick verkar 1 uppfylla den naiva definitionen av ett primtal; delar jämnt med 1 och sig självt (som är 1). Matematiker har så sent som i mitten av 1900-talet ansett 1 som ett primtal, men har sedan dess uteslutits det som primtal av olika skäl (ger komplikationer för [[aritmetikens fundamentalsats]] exempelvis).<ref>{{Webbref|url=https://www.youtube.com/watch?v=IQofiPqhJ_s|titel=1 and Prime Numbers|hämtdatum=13 augusti 2020|datum=3 februari 2012|utgivare=[[YouTube]]|språk=engelska|format=videofil|efternamn=Grime|förnamn=James|författarlänk=James Grime|verk=[[Numberphile]]|arkivurl=https://archive.today/20170807153656/https://www.youtube.com/watch?v=IQofiPqhJ_s|arkivdatum=2017-08-07}}</ref>}}

== De 1 000 första primtalen ==

Ett primtal är ett naturligt tal som är större än [[1 (tal)|1]] och som inte är en [[Produkt (matematik)|produkt]] av två andra mindre naturliga tal.<ref>{{Bokref|titel=List of prime numbers from 1 to 10,006,721.|url=http://worldcat.org/oclc/859805174|utgivare=Hafner|datum=1956|hämtdatum=13 augusti 2020|oclc=859805174|efternamn=Lehmer|förnamn=Derrick Norman|språk=engelska|utgivningsort=New York|författarlänk=Derrick Norman Lehmer|libris=2768728|id=[[Open Library|OL]] [https://openlibrary.org/books/OL6203229M/List_of_prime_numbers_from_1_to_10_006_721. 6203229M].|år=|sid=}}</ref>

{| class="wikitable mw-collapsible mw-collapsed" style="text-align: center; width: 100%;"
! colspan="21" | Tabell över de 1 000 första primtalen {{Ej fet|{{OEIS|A000040}}}}
|-
! {{Nowrap|1 – 20}}
| [[2 (tal)|2]]
| [[3 (tal)|3]]
| [[5 (tal)|5]]
| [[7 (tal)|7]]
| [[11 (tal)|11]]
| [[13 (tal)|13]]
| [[17 (tal)|17]]
| [[19 (tal)|19]]
| [[23 (tal)|23]]
| [[29 (tal)|29]]
| [[31 (tal)|31]]
| [[37 (tal)|37]]
| [[41 (tal)|41]]
| [[43 (tal)|43]]
| [[47 (tal)|47]]
| [[53 (tal)|53]]
| [[59 (tal)|59]]
| [[61 (tal)|61]]
| [[67 (tal)|67]]
| [[71 (tal)|71]]
|-
! {{Nowrap|21 – 40}}
| [[73 (tal)|73]]
| [[79 (tal)|79]]
| [[83 (tal)|83]]
| [[89 (tal)|89]]
| [[97 (tal)|97]]
| [[101 (tal)|101]]
| [[103 (tal)|103]]
| [[107 (tal)|107]]
| [[109 (tal)|109]]
| [[113 (tal)|113]]
| [[127 (tal)|127]]
| [[131 (tal)|131]]
| [[137 (tal)|137]]
| [[139 (tal)|139]]
| [[149 (tal)|149]]
| [[151 (tal)|151]]
| [[157 (tal)|157]]
| [[163 (tal)|163]]
| [[167 (tal)|167]]
| [[173 (tal)|173]]
|-
! 41 – 60
| [[179 (tal)|179]]
| [[181 (tal)|181]]
| [[191 (tal)|191]]
| [[193 (tal)|193]]
| [[197 (tal)|197]]
| [[199 (tal)|199]]
| [[211 (tal)|211]]
| [[223 (tal)|223]]
| [[227 (tal)|227]]
| [[229 (tal)|229]]
| [[233 (tal)|233]]
| [[239 (tal)|239]]
| [[241 (tal)|241]]
| [[251 (tal)|251]]
| [[257 (tal)|257]]
| [[263 (tal)|263]]
| [[269 (tal)|269]]
| [[271 (tal)|271]]
| [[277 (tal)|277]]
| [[281 (tal)|281]]
|-
! 61 – 80
| [[283 (tal)|283]]
| [[293 (tal)|293]]
| [[307 (tal)|307]]
| [[311 (tal)|311]]
| [[313 (tal)|313]]
| [[317 (tal)|317]]
| [[331 (tal)|331]]
| [[337 (tal)|337]]
| [[347 (tal)|347]]
| [[349 (tal)|349]]
| [[353 (tal)|353]]
| [[359 (tal)|359]]
| [[367 (tal)|367]]
| [[373 (tal)|373]]
| [[379 (tal)|379]]
| [[383 (tal)|383]]
| [[389 (tal)|389]]
| [[397 (tal)|397]]
| [[401 (tal)|401]]
| [[409 (tal)|409]]
|-
! 81 – 100
| [[419 (tal)|419]]
| [[421 (tal)|421]]
| [[431 (tal)|431]]
| [[433 (tal)|433]]
| [[439 (tal)|439]]
| [[443 (tal)|443]]
| [[449 (tal)|449]]
| [[457 (tal)|457]]
| [[461 (tal)|461]]
| [[463 (tal)|463]]
| [[467 (tal)|467]]
| [[479 (tal)|479]]
| [[487 (tal)|487]]
| [[491 (tal)|491]]
| [[499 (tal)|499]]
| [[503 (tal)|503]]
| [[509 (tal)|509]]
| [[521 (tal)|521]]
| [[523 (tal)|523]]
| [[541 (tal)|541]]
|-
! 101 – 120
| [[547 (tal)|547]]
| [[557 (tal)|557]]
| [[563 (tal)|563]]
| [[569 (tal)|569]]
| [[571 (tal)|571]]
| [[577 (tal)|577]]
| [[587 (tal)|587]]
| [[593 (tal)|593]]
| [[599 (tal)|599]]
| [[601 (tal)|601]]
| [[607 (tal)|607]]
| [[613 (tal)|613]]
| [[617 (tal)|617]]
| [[619 (tal)|619]]
| [[631 (tal)|631]]
| [[641 (tal)|641]]
| [[643 (tal)|643]]
| [[647 (tal)|647]]
| [[653 (tal)|653]]
| [[659 (tal)|659]]
|-
! 121 – 140
| [[661 (tal)|661]]
| [[673 (tal)|673]]
| [[677 (tal)|677]]
| [[683 (tal)|683]]
| [[691 (tal)|691]]
| [[701 (tal)|701]]
| [[709 (tal)|709]]
| [[719 (tal)|719]]
| [[727 (tal)|727]]
| [[733 (tal)|733]]
| [[739 (tal)|739]]
| [[743 (tal)|743]]
| [[751 (tal)|751]]
| [[757 (tal)|757]]
| [[761 (tal)|761]]
| [[769 (tal)|769]]
| [[773 (tal)|773]]
| [[787 (tal)|787]]
| [[797 (tal)|797]]
| [[809 (tal)|809]]
|-
! 141 – 160
| [[811 (tal)|811]]
| [[821 (tal)|821]]
| [[823 (tal)|823]]
| [[827 (tal)|827]]
| [[829 (tal)|829]]
| [[839 (tal)|839]]
| [[853 (tal)|853]]
| [[857 (tal)|857]]
| [[859 (tal)|859]]
| [[863 (tal)|863]]
| [[877 (tal)|877]]
| [[881 (tal)|881]]
| [[883 (tal)|883]]
| [[887 (tal)|887]]
| [[907 (tal)|907]]
| [[911 (tal)|911]]
| [[919 (tal)|919]]
| [[929 (tal)|929]]
| [[937 (tal)|937]]
| [[941 (tal)|941]]
|-
! 161 – 180
| [[947 (tal)|947]]
| [[953 (tal)|953]]
| [[967 (tal)|967]]
| [[971 (tal)|971]]
| [[977 (tal)|977]]
| [[983 (tal)|983]]
| [[991 (tal)|991]]
| [[997 (tal)|997]]
| [[1009 (tal)|1009]]
| [[1013 (tal)|1013]]
| [[1019 (tal)|1019]]
| [[1021 (tal)|1021]]
| [[1031 (tal)|1031]]
| [[1033 (tal)|1033]]
| [[1039 (tal)|1039]]
| [[1049 (tal)|1049]]
| [[1051 (tal)|1051]]
| [[1061 (tal)|1061]]
| [[1063 (tal)|1063]]
| [[1069 (tal)|1069]]
|-
! 181 – 200
| [[1087 (tal)|1087]]
| [[1091 (tal)|1091]]
| [[1093 (tal)|1093]]
| [[1097 (tal)|1097]]
| [[1103 (tal)|1103]]
| [[1109 (tal)|1109]]
| [[1117 (tal)|1117]]
| [[1123 (tal)|1123]]
| [[1129 (tal)|1129]]
| [[1151 (tal)|1151]]
| [[1153 (tal)|1153]]
| [[1163 (tal)|1163]]
| [[1171 (tal)|1171]]
| [[1181 (tal)|1181]]
| [[1187 (tal)|1187]]
| [[1193 (tal)|1193]]
| [[1201 (tal)|1201]]
| [[1213 (tal)|1213]]
| [[1217 (tal)|1217]]
| [[1223 (tal)|1223]]
|-
! 201 – 220
| [[1229 (tal)|1229]]
| [[1231 (tal)|1231]]
| [[1237 (tal)|1237]]
| [[1249 (tal)|1249]]
| [[1259 (tal)|1259]]
| [[1277 (tal)|1277]]
| [[1279 (tal)|1279]]
| [[1283 (tal)|1283]]
| [[1289 (tal)|1289]]
| [[1291 (tal)|1291]]
| [[1297 (tal)|1297]]
| [[1301 (tal)|1301]]
| [[1303 (tal)|1303]]
| [[1307 (tal)|1307]]
| [[1319 (tal)|1319]]
| [[1321 (tal)|1321]]
| [[1327 (tal)|1327]]
| [[1361 (tal)|1361]]
| [[1367 (tal)|1367]]
| [[1373 (tal)|1373]]
|-
! 221 – 240
| [[1381 (tal)|1381]]
| [[1399 (tal)|1399]]
| [[1409 (tal)|1409]]
| [[1423 (tal)|1423]]
| [[1427 (tal)|1427]]
| [[1429 (tal)|1429]]
| [[1433 (tal)|1433]]
| [[1439 (tal)|1439]]
| [[1447 (tal)|1447]]
| [[1451 (tal)|1451]]
| [[1453 (tal)|1453]]
| [[1459 (tal)|1459]]
| [[1471 (tal)|1471]]
| [[1481 (tal)|1481]]
| [[1483 (tal)|1483]]
| [[1487 (tal)|1487]]
| [[1489 (tal)|1489]]
| [[1493 (tal)|1493]]
| [[1499 (tal)|1499]]
| [[1511 (tal)|1511]]
|-
! 241 – 260
| [[1523 (tal)|1523]]
| [[1531 (tal)|1531]]
| [[1543 (tal)|1543]]
| [[1549 (tal)|1549]]
| [[1553 (tal)|1553]]
| [[1559 (tal)|1559]]
| [[1567 (tal)|1567]]
| [[1571 (tal)|1571]]
| [[1579 (tal)|1579]]
| [[1583 (tal)|1583]]
| [[1597 (tal)|1597]]
| [[1601 (tal)|1601]]
| [[1607 (tal)|1607]]
| [[1609 (tal)|1609]]
| [[1613 (tal)|1613]]
| [[1619 (tal)|1619]]
| [[1621 (tal)|1621]]
| [[1627 (tal)|1627]]
| [[1637 (tal)|1637]]
| [[1657 (tal)|1657]]
|-
! 261 – 280
| [[1663 (tal)|1663]]
| [[1667 (tal)|1667]]
| [[1669 (tal)|1669]]
| [[1693 (tal)|1693]]
| [[1697 (tal)|1697]]
| [[1699 (tal)|1699]]
| [[1709 (tal)|1709]]
| [[1721 (tal)|1721]]
| [[1723 (tal)|1723]]
| [[1733 (tal)|1733]]
| [[1741 (tal)|1741]]
| [[1747 (tal)|1747]]
| [[1753 (tal)|1753]]
| [[1759 (tal)|1759]]
| [[1777 (tal)|1777]]
| [[1783 (tal)|1783]]
| [[1787 (tal)|1787]]
| [[1789 (tal)|1789]]
| [[1801 (tal)|1801]]
| [[1811 (tal)|1811]]
|-
! 281 – 300
| [[1823 (tal)|1823]]
| [[1831 (tal)|1831]]
| [[1847 (tal)|1847]]
| [[1861 (tal)|1861]]
| [[1867 (tal)|1867]]
| [[1871 (tal)|1871]]
| [[1873 (tal)|1873]]
| [[1877 (tal)|1877]]
| [[1879 (tal)|1879]]
| [[1889 (tal)|1889]]
| [[1901 (tal)|1901]]
| [[1907 (tal)|1907]]
| [[1913 (tal)|1913]]
| [[1931 (tal)|1931]]
| [[1933 (tal)|1933]]
| [[1949 (tal)|1949]]
| [[1951 (tal)|1951]]
| [[1973 (tal)|1973]]
| [[1979 (tal)|1979]]
| [[1987 (tal)|1987]]
|-
! 301 – 320
| [[1993 (tal)|1993]]
| [[1997 (tal)|1997]]
| [[1999 (tal)|1999]]
| [[2003 (tal)|2003]]
| [[2011 (tal)|2011]]
| [[2017 (tal)|2017]]
| [[2027 (tal)|2027]]
| [[2029 (tal)|2029]]
| [[2039 (tal)|2039]]
| [[2053 (tal)|2053]]
| [[2063 (tal)|2063]]
| [[2069 (tal)|2069]]
| [[2081 (tal)|2081]]
| [[2083 (tal)|2083]]
| [[2087 (tal)|2087]]
| [[2089 (tal)|2089]]
| [[2099 (tal)|2099]]
| [[2111 (tal)|2111]]
| [[2113 (tal)|2113]]
| [[2129 (tal)|2129]]
|-
! 321 – 340
| [[2131 (tal)|2131]]
| [[2137 (tal)|2137]]
| [[2141 (tal)|2141]]
| [[2143 (tal)|2143]]
| [[2153 (tal)|2153]]
| [[2161 (tal)|2161]]
| [[2179 (tal)|2179]]
| [[2203 (tal)|2203]]
| [[2207 (tal)|2207]]
| [[2213 (tal)|2213]]
| [[2221 (tal)|2221]]
| [[2237 (tal)|2237]]
| [[2239 (tal)|2239]]
| [[2243 (tal)|2243]]
| [[2251 (tal)|2251]]
| [[2267 (tal)|2267]]
| [[2269 (tal)|2269]]
| [[2273 (tal)|2273]]
| [[2281 (tal)|2281]]
| [[2287 (tal)|2287]]
|-
! 341 – 360
| [[2293 (tal)|2293]]
| [[2297 (tal)|2297]]
| [[2309 (tal)|2309]]
| [[2311 (tal)|2311]]
| [[2333 (tal)|2333]]
| [[2339 (tal)|2339]]
| [[2341 (tal)|2341]]
| [[2347 (tal)|2347]]
| [[2351 (tal)|2351]]
| [[2357 (tal)|2357]]
| [[2371 (tal)|2371]]
| [[2377 (tal)|2377]]
| [[2381 (tal)|2381]]
| [[2383 (tal)|2383]]
| [[2389 (tal)|2389]]
| [[2393 (tal)|2393]]
| [[2399 (tal)|2399]]
| [[2411 (tal)|2411]]
| [[2417 (tal)|2417]]
| [[2423 (tal)|2423]]
|-
! 361 – 380
| [[2437 (tal)|2437]]
| [[2441 (tal)|2441]]
| [[2447 (tal)|2447]]
| [[2459 (tal)|2459]]
| [[2467 (tal)|2467]]
| [[2473 (tal)|2473]]
| [[2477 (tal)|2477]]
| [[2503 (tal)|2503]]
| [[2521 (tal)|2521]]
| [[2531 (tal)|2531]]
| [[2539 (tal)|2539]]
| [[2543 (tal)|2543]]
| [[2549 (tal)|2549]]
| [[2551 (tal)|2551]]
| [[2557 (tal)|2557]]
| [[2579 (tal)|2579]]
| [[2591 (tal)|2591]]
| [[2593 (tal)|2593]]
| [[2609 (tal)|2609]]
| [[2617 (tal)|2617]]
|-
! 381 – 400
| [[2621 (tal)|2621]]
| [[2633 (tal)|2633]]
| [[2647 (tal)|2647]]
| [[2657 (tal)|2657]]
| [[2659 (tal)|2659]]
| [[2663 (tal)|2663]]
| [[2671 (tal)|2671]]
| [[2677 (tal)|2677]]
| [[2683 (tal)|2683]]
| [[2687 (tal)|2687]]
| [[2689 (tal)|2689]]
| [[2693 (tal)|2693]]
| [[2699 (tal)|2699]]
| [[2707 (tal)|2707]]
| [[2711 (tal)|2711]]
| [[2713 (tal)|2713]]
| [[2719 (tal)|2719]]
| [[2729 (tal)|2729]]
| [[2731 (tal)|2731]]
| [[2741 (tal)|2741]]
|-
! 401 – 420
| [[2749 (tal)|2749]]
| [[2753 (tal)|2753]]
| [[2767 (tal)|2767]]
| [[2777 (tal)|2777]]
| [[2789 (tal)|2789]]
| [[2791 (tal)|2791]]
| [[2797 (tal)|2797]]
| [[2801 (tal)|2801]]
| [[2803 (tal)|2803]]
| [[2819 (tal)|2819]]
| [[2833 (tal)|2833]]
| [[2837 (tal)|2837]]
| [[2843 (tal)|2843]]
| [[2851 (tal)|2851]]
| [[2857 (tal)|2857]]
| [[2861 (tal)|2861]]
| [[2879 (tal)|2879]]
| [[2887 (tal)|2887]]
| [[2897 (tal)|2897]]
| [[2903 (tal)|2903]]
|-
! 421 – 440
| [[2909 (tal)|2909]]
| [[2917 (tal)|2917]]
| [[2927 (tal)|2927]]
| [[2939 (tal)|2939]]
| [[2953 (tal)|2953]]
| [[2957 (tal)|2957]]
| [[2963 (tal)|2963]]
| [[2969 (tal)|2969]]
| [[2971 (tal)|2971]]
| [[2999 (tal)|2999]]
| [[3001 (tal)|3001]]
| [[3011 (tal)|3011]]
| [[3019 (tal)|3019]]
| [[3023 (tal)|3023]]
| [[3037 (tal)|3037]]
| [[3041 (tal)|3041]]
| [[3049 (tal)|3049]]
| [[3061 (tal)|3061]]
| [[3067 (tal)|3067]]
| [[3079 (tal)|3079]]
|-
! 441 – 460
| [[3083 (tal)|3083]]
| [[3089 (tal)|3089]]
| [[3109 (tal)|3109]]
| [[3119 (tal)|3119]]
| [[3121 (tal)|3121]]
| [[3137 (tal)|3137]]
| [[3163 (tal)|3163]]
| [[3167 (tal)|3167]]
| [[3169 (tal)|3169]]
| [[3181 (tal)|3181]]
| [[3187 (tal)|3187]]
| [[3191 (tal)|3191]]
| [[3203 (tal)|3203]]
| [[3209 (tal)|3209]]
| [[3217 (tal)|3217]]
| [[3221 (tal)|3221]]
| [[3229 (tal)|3229]]
| [[3251 (tal)|3251]]
| [[3253 (tal)|3253]]
| [[3257 (tal)|3257]]
|-
! 461 – 480
| [[3259 (tal)|3259]]
| [[3271 (tal)|3271]]
| [[3299 (tal)|3299]]
| [[3301 (tal)|3301]]
| [[3307 (tal)|3307]]
| [[3313 (tal)|3313]]
| [[3319 (tal)|3319]]
| [[3323 (tal)|3323]]
| [[3329 (tal)|3329]]
| [[3331 (tal)|3331]]
| [[3343 (tal)|3343]]
| [[3347 (tal)|3347]]
| [[3359 (tal)|3359]]
| [[3361 (tal)|3361]]
| [[3371 (tal)|3371]]
| [[3373 (tal)|3373]]
| [[3389 (tal)|3389]]
| [[3391 (tal)|3391]]
| [[3407 (tal)|3407]]
| [[3413 (tal)|3413]]
|-
! 481 – 500
| [[3433 (tal)|3433]]
| [[3449 (tal)|3449]]
| [[3457 (tal)|3457]]
| [[3461 (tal)|3461]]
| [[3463 (tal)|3463]]
| [[3467 (tal)|3467]]
| [[3469 (tal)|3469]]
| [[3491 (tal)|3491]]
| [[3499 (tal)|3499]]
| [[3511 (tal)|3511]]
| [[3517 (tal)|3517]]
| [[3527 (tal)|3527]]
| [[3529 (tal)|3529]]
| [[3533 (tal)|3533]]
| [[3539 (tal)|3539]]
| [[3541 (tal)|3541]]
| [[3547 (tal)|3547]]
| [[3557 (tal)|3557]]
| [[3559 (tal)|3559]]
| [[3571 (tal)|3571]]
|-
! 501 – 520
| [[3581 (tal)|3581]]
| [[3583 (tal)|3583]]
| [[3593 (tal)|3593]]
| [[3607 (tal)|3607]]
| [[3613 (tal)|3613]]
| [[3617 (tal)|3617]]
| [[3623 (tal)|3623]]
| [[3631 (tal)|3631]]
| [[3637 (tal)|3637]]
| [[3643 (tal)|3643]]
| [[3659 (tal)|3659]]
| [[3671 (tal)|3671]]
| [[3673 (tal)|3673]]
| [[3677 (tal)|3677]]
| [[3691 (tal)|3691]]
| [[3697 (tal)|3697]]
| [[3701 (tal)|3701]]
| [[3709 (tal)|3709]]
| [[3719 (tal)|3719]]
| [[3727 (tal)|3727]]
|-
! 521 – 540
| [[3733 (tal)|3733]]
| [[3739 (tal)|3739]]
| [[3761 (tal)|3761]]
| [[3767 (tal)|3767]]
| [[3769 (tal)|3769]]
| [[3779 (tal)|3779]]
| [[3793 (tal)|3793]]
| [[3797 (tal)|3797]]
| [[3803 (tal)|3803]]
| [[3821 (tal)|3821]]
| [[3823 (tal)|3823]]
| [[3833 (tal)|3833]]
| [[3847 (tal)|3847]]
| [[3851 (tal)|3851]]
| [[3853 (tal)|3853]]
| [[3863 (tal)|3863]]
| [[3877 (tal)|3877]]
| [[3881 (tal)|3881]]
| [[3889 (tal)|3889]]
| [[3907 (tal)|3907]]
|-
! 541 – 560
| [[3911 (tal)|3911]]
| [[3917 (tal)|3917]]
| [[3919 (tal)|3919]]
| [[3923 (tal)|3923]]
| [[3929 (tal)|3929]]
| [[3931 (tal)|3931]]
| [[3943 (tal)|3943]]
| [[3947 (tal)|3947]]
| [[3967 (tal)|3967]]
| [[3989 (tal)|3989]]
| [[4001 (tal)|4001]]
| [[4003 (tal)|4003]]
| [[4007 (tal)|4007]]
| [[4013 (tal)|4013]]
| [[4019 (tal)|4019]]
| [[4021 (tal)|4021]]
| [[4027 (tal)|4027]]
| [[4049 (tal)|4049]]
| [[4051 (tal)|4051]]
| [[4057 (tal)|4057]]
|-
! 561 – 580
| [[4073 (tal)|4073]]
| [[4079 (tal)|4079]]
| [[4091 (tal)|4091]]
| [[4093 (tal)|4093]]
| [[4099 (tal)|4099]]
| [[4111 (tal)|4111]]
| [[4127 (tal)|4127]]
| [[4129 (tal)|4129]]
| [[4133 (tal)|4133]]
| [[4139 (tal)|4139]]
| [[4153 (tal)|4153]]
| [[4157 (tal)|4157]]
| [[4159 (tal)|4159]]
| [[4177 (tal)|4177]]
| [[4201 (tal)|4201]]
| [[4211 (tal)|4211]]
| [[4217 (tal)|4217]]
| [[4219 (tal)|4219]]
| [[4229 (tal)|4229]]
| [[4231 (tal)|4231]]
|-
! 581 – 600
| [[4241 (tal)|4241]]
| [[4243 (tal)|4243]]
| [[4253 (tal)|4253]]
| [[4259 (tal)|4259]]
| [[4261 (tal)|4261]]
| [[4271 (tal)|4271]]
| [[4273 (tal)|4273]]
| [[4283 (tal)|4283]]
| [[4289 (tal)|4289]]
| [[4297 (tal)|4297]]
| [[4327 (tal)|4327]]
| [[4337 (tal)|4337]]
| [[4339 (tal)|4339]]
| [[4349 (tal)|4349]]
| [[4357 (tal)|4357]]
| [[4363 (tal)|4363]]
| [[4373 (tal)|4373]]
| [[4391 (tal)|4391]]
| [[4397 (tal)|4397]]
| [[4209 (tal)|4409]]
|-
! 601 – 620
| [[4421 (tal)|4421]]
| [[4423 (tal)|4423]]
| [[4441 (tal)|4441]]
| [[4447 (tal)|4447]]
| [[4451 (tal)|4451]]
| [[4457 (tal)|4457]]
| [[4463 (tal)|4463]]
| [[4481 (tal)|4481]]
| [[4483 (tal)|4483]]
| [[4493 (tal)|4493]]
| [[4507 (tal)|4507]]
| [[4513 (tal)|4513]]
| [[4517 (tal)|4517]]
| [[4519 (tal)|4519]]
| [[4523 (tal)|4523]]
| [[4547 (tal)|4547]]
| [[4549 (tal)|4549]]
| [[4561 (tal)|4561]]
| [[4567 (tal)|4567]]
| [[4583 (tal)|4583]]
|-
! 621 – 640
| [[4591 (tal)|4591]]
| [[4597 (tal)|4597]]
| [[4603 (tal)|4603]]
| [[4621 (tal)|4621]]
| [[4637 (tal)|4637]]
| [[4639 (tal)|4639]]
| [[4643 (tal)|4643]]
| [[4649 (tal)|4649]]
| [[4651 (tal)|4651]]
| [[4657 (tal)|4657]]
| [[4663 (tal)|4663]]
| [[4673 (tal)|4673]]
| [[4679 (tal)|4679]]
| [[4691 (tal)|4691]]
| [[4703 (tal)|4703]]
| [[4721 (tal)|4721]]
| [[4723 (tal)|4723]]
| [[4729 (tal)|4729]]
| [[4733 (tal)|4733]]
| [[4751 (tal)|4751]]
|-
! 641 – 660
| [[4759 (tal)|4759]]
| [[4783 (tal)|4783]]
| [[4787 (tal)|4787]]
| [[4789 (tal)|4789]]
| [[4793 (tal)|4793]]
| [[4799 (tal)|4799]]
| [[4801 (tal)|4801]]
| [[4813 (tal)|4813]]
| [[4817 (tal)|4817]]
| [[4831 (tal)|4831]]
| [[4861 (tal)|4861]]
| [[4871 (tal)|4871]]
| [[4877 (tal)|4877]]
| [[4889 (tal)|4889]]
| [[4903 (tal)|4903]]
| [[4909 (tal)|4909]]
| [[4919 (tal)|4919]]
| [[4931 (tal)|4931]]
| [[4933 (tal)|4933]]
| [[4937 (tal)|4937]]
|-
! 661 – 680
| [[4943 (tal)|4943]]
| [[4951 (tal)|4951]]
| [[4957 (tal)|4957]]
| [[4967 (tal)|4967]]
| [[4969 (tal)|4969]]
| [[4973 (tal)|4973]]
| [[4987 (tal)|4987]]
| [[4993 (tal)|4993]]
| [[4999 (tal)|4999]]
| [[5003 (tal)|5003]]
| [[5009 (tal)|5009]]
| [[5011 (tal)|5011]]
| [[5021 (tal)|5021]]
| [[5023 (tal)|5023]]
| [[5039 (tal)|5039]]
| [[5051 (tal)|5051]]
| [[5059 (tal)|5059]]
| [[5077 (tal)|5077]]
| [[5081 (tal)|5081]]
| [[5087 (tal)|5087]]
|-
! 681 – 700
| [[5099 (tal)|5099]]
| [[5101 (tal)|5101]]
| [[5107 (tal)|5107]]
| [[5113 (tal)|5113]]
| [[5119 (tal)|5119]]
| [[5147 (tal)|5147]]
| [[5153 (tal)|5153]]
| [[5167 (tal)|5167]]
| [[5171 (tal)|5171]]
| [[5179 (tal)|5179]]
| [[5189 (tal)|5189]]
| [[5197 (tal)|5197]]
| [[5209 (tal)|5209]]
| [[5227 (tal)|5227]]
| [[5231 (tal)|5231]]
| [[5233 (tal)|5233]]
| [[5237 (tal)|5237]]
| [[5261 (tal)|5261]]
| [[5273 (tal)|5273]]
| [[5279 (tal)|5279]]
|-
! 701 – 720
| [[5281 (tal)|5281]]
| [[5297 (tal)|5297]]
| [[5303 (tal)|5303]]
| [[5309 (tal)|5309]]
| [[5323 (tal)|5323]]
| [[5333 (tal)|5333]]
| [[5347 (tal)|5347]]
| [[5351 (tal)|5351]]
| [[5381 (tal)|5381]]
| [[5387 (tal)|5387]]
| [[5393 (tal)|5393]]
| [[5399 (tal)|5399]]
| [[5407 (tal)|5407]]
| [[5413 (tal)|5413]]
| [[5417 (tal)|5417]]
| [[5419 (tal)|5419]]
| [[5431 (tal)|5431]]
| [[5437 (tal)|5437]]
| [[5441 (tal)|5441]]
| [[5443 (tal)|5443]]
|-
! 721 – 740
| [[5449 (tal)|5449]]
| [[5471 (tal)|5471]]
| [[5477 (tal)|5477]]
| [[5479 (tal)|5479]]
| [[5483 (tal)|5483]]
| [[5501 (tal)|5501]]
| [[5503 (tal)|5503]]
| [[5507 (tal)|5507]]
| [[5519 (tal)|5519]]
| [[5521 (tal)|5521]]
| [[5527 (tal)|5527]]
| [[5531 (tal)|5531]]
| [[5557 (tal)|5557]]
| [[5563 (tal)|5563]]
| [[5569 (tal)|5569]]
| [[5573 (tal)|5573]]
| [[5581 (tal)|5581]]
| [[5591 (tal)|5591]]
| [[5623 (tal)|5623]]
| [[5639 (tal)|5639]]
|-
! 741 – 760
| [[5641 (tal)|5641]]
| [[5647 (tal)|5647]]
| [[5651 (tal)|5651]]
| [[5653 (tal)|5653]]
| [[5657 (tal)|5657]]
| [[5659 (tal)|5659]]
| [[5669 (tal)|5669]]
| [[5683 (tal)|5683]]
| [[5689 (tal)|5689]]
| [[5693 (tal)|5693]]
| [[5701 (tal)|5701]]
| [[5711 (tal)|5711]]
| [[5717 (tal)|5717]]
| [[5737 (tal)|5737]]
| [[5741 (tal)|5741]]
| [[5743 (tal)|5743]]
| [[5749 (tal)|5749]]
| [[5779 (tal)|5779]]
| [[5783 (tal)|5783]]
| [[5791 (tal)|5791]]
|-
! 761 – 780
| [[5801 (tal)|5801]]
| [[5807 (tal)|5807]]
| [[5813 (tal)|5813]]
| [[5821 (tal)|5821]]
| [[5827 (tal)|5827]]
| [[5839 (tal)|5839]]
| [[5843 (tal)|5843]]
| [[5949 (tal)|5849]]
| [[5851 (tal)|5851]]
| [[5857 (tal)|5857]]
| [[5861 (tal)|5861]]
| [[5867 (tal)|5867]]
| [[5869 (tal)|5869]]
| [[5879 (tal)|5879]]
| [[5881 (tal)|5881]]
| [[5897 (tal)|5897]]
| [[5903 (tal)|5903]]
| [[5923 (tal)|5923]]
| [[5927 (tal)|5927]]
| [[5939 (tal)|5939]]
|-
! {{Nowrap|781 – 800}}
| [[5953 (tal)|5953]]
| [[5981 (tal)|5981]]
| [[5987 (tal)|5987]]
| [[6007 (tal)|6007]]
| [[6011 (tal)|6011]]
| [[6029 (tal)|6029]]
| [[6037 (tal)|6037]]
| [[6043 (tal)|6043]]
| [[6047 (tal)|6047]]
| [[6053 (tal)|6053]]
| [[6067 (tal)|6067]]
| [[6073 (tal)|6073]]
| [[6079 (tal)|6079]]
| [[6089 (tal)|6089]]
| [[6091 (tal)|6091]]
| [[6101 (tal)|6101]]
| [[6113 (tal)|6113]]
| [[6121 (tal)|6121]]
| [[6131 (tal)|6131]]
| [[6133 (tal)|6133]]
|-
! {{Nowrap|801 – 820}}
| [[6143 (tal)|6143]]
| [[6151 (tal)|6151]]
| [[6163 (tal)|6163]]
| [[6173 (tal)|6173]]
| [[6197 (tal)|6197]]
| [[6199 (tal)|6199]]
| [[6203 (tal)|6203]]
| [[6211 (tal)|6211]]
| [[6217 (tal)|6217]]
| [[6221 (tal)|6221]]
| [[6229 (tal)|6229]]
| [[6247 (tal)|6247]]
| [[6257 (tal)|6257]]
| [[6263 (tal)|6263]]
| [[6269 (tal)|6269]]
| [[6271 (tal)|6271]]
| [[6277 (tal)|6277]]
| [[6287 (tal)|6287]]
| [[6299 (tal)|6299]]
| [[6301 (tal)|6301]]
|-
! {{Nowrap|821 – 840}}
| [[6311 (tal)|6311]]
| [[6317 (tal)|6317]]
| [[6323 (tal)|6323]]
| [[6329 (tal)|6329]]
| [[6337 (tal)|6337]]
| [[6343 (tal)|6343]]
| [[6353 (tal)|6353]]
| [[6359 (tal)|6359]]
| [[6361 (tal)|6361]]
| [[6367 (tal)|6367]]
| [[6373 (tal)|6373]]
| [[6379 (tal)|6379]]
| [[6389 (tal)|6389]]
| [[6397 (tal)|6397]]
| [[6421 (tal)|6421]]
| [[6427 (tal)|6427]]
| [[6449 (tal)|6449]]
| [[6451 (tal)|6451]]
| [[6469 (tal)|6469]]
| [[6473 (tal)|6473]]
|-
! {{Nowrap|841 – 860}}
| [[6481 (tal)|6481]]
| [[6491 (tal)|6491]]
| [[6521 (tal)|6521]]
| [[6529 (tal)|6529]]
| [[6547 (tal)|6547]]
| [[6551 (tal)|6551]]
| [[6553 (tal)|6553]]
| [[6563 (tal)|6563]]
| [[6569 (tal)|6569]]
| [[6571 (tal)|6571]]
| [[6577 (tal)|6577]]
| [[6581 (tal)|6581]]
| [[6599 (tal)|6599]]
| [[6607 (tal)|6607]]
| [[6619 (tal)|6619]]
| [[6637 (tal)|6637]]
| [[6653 (tal)|6653]]
| [[6659 (tal)|6659]]
| [[6661 (tal)|6661]]
| [[6673 (tal)|6673]]
|-
! {{Nowrap|861 – 880}}
| [[6679 (tal)|6679]]
| [[6689 (tal)|6689]]
| [[6691 (tal)|6691]]
| [[6701 (tal)|6701]]
| [[6703 (tal)|6703]]
| [[6709 (tal)|6709]]
| [[6719 (tal)|6719]]
| [[6733 (tal)|6733]]
| [[6737 (tal)|6737]]
| [[6761 (tal)|6761]]
| [[6763 (tal)|6763]]
| [[6779 (tal)|6779]]
| [[6781 (tal)|6781]]
| [[6791 (tal)|6791]]
| [[6793 (tal)|6793]]
| [[6803 (tal)|6803]]
| [[6823 (tal)|6823]]
| [[6827 (tal)|6827]]
| [[6829 (tal)|6829]]
| [[6833 (tal)|6833]]
|-
! {{Nowrap|881 – 900}}
| [[6841 (tal)|6841]]
| [[6857 (tal)|6857]]
| [[6863 (tal)|6863]]
| [[6869 (tal)|6869]]
| [[6871 (tal)|6871]]
| [[6883 (tal)|6883]]
| [[6899 (tal)|6899]]
| [[6907 (tal)|6907]]
| [[6911 (tal)|6911]]
| [[6917 (tal)|6917]]
| [[6947 (tal)|6947]]
| [[6949 (tal)|6949]]
| [[6959 (tal)|6959]]
| [[6961 (tal)|6961]]
| [[6967 (tal)|6967]]
| [[6971 (tal)|6971]]
| [[6977 (tal)|6977]]
| [[6983 (tal)|6983]]
| [[6991 (tal)|6991]]
| [[6997 (tal)|6997]]
|-
! {{Nowrap|901 – 920}}
| [[7001 (tal)|7001]]
| [[7013 (tal)|7013]]
| [[7019 (tal)|7019]]
| [[7027 (tal)|7027]]
| [[7039 (tal)|7039]]
| [[7043 (tal)|7043]]
| [[7057 (tal)|7057]]
| [[7069 (tal)|7069]]
| [[7079 (tal)|7079]]
| [[7103 (tal)|7103]]
| [[7109 (tal)|7109]]
| [[7121 (tal)|7121]]
| [[7127 (tal)|7127]]
| [[7129 (tal)|7129]]
| [[7151 (tal)|7151]]
| [[7159 (tal)|7159]]
| [[7177 (tal)|7177]]
| [[7187 (tal)|7187]]
| [[7193 (tal)|7193]]
| [[7207 (tal)|7207]]
|-
! {{Nowrap|921 – 940}}
| [[7211 (tal)|7211]]
| [[7213 (tal)|7213]]
| [[7219 (tal)|7219]]
| [[7229 (tal)|7229]]
| [[7237 (tal)|7237]]
| [[7243 (tal)|7243]]
| [[7247 (tal)|7247]]
| [[7253 (tal)|7253]]
| [[7283 (tal)|7283]]
| [[7297 (tal)|7297]]
| [[7307 (tal)|7307]]
| [[7309 (tal)|7309]]
| [[7321 (tal)|7321]]
| [[7331 (tal)|7331]]
| [[7333 (tal)|7333]]
| [[7349 (tal)|7349]]
| [[7351 (tal)|7351]]
| [[7369 (tal)|7369]]
| [[7393 (tal)|7393]]
| [[7411 (tal)|7411]]
|-
! {{Nowrap|941 – 960}}
| [[7417 (tal)|7417]]
| [[7433 (tal)|7433]]
| [[7451 (tal)|7451]]
| [[7557 (tal)|7457]]
| [[7459 (tal)|7459]]
| [[7477 (tal)|7477]]
| [[7481 (tal)|7481]]
| [[7487 (tal)|7487]]
| [[7489 (tal)|7489]]
| [[7499 (tal)|7499]]
| [[7507 (tal)|7507]]
| [[7517 (tal)|7517]]
| [[7523 (tal)|7523]]
| [[7529 (tal)|7529]]
| [[7537 (tal)|7537]]
| [[7541 (tal)|7541]]
| [[7547 (tal)|7547]]
| [[7549 (tal)|7549]]
| [[7559 (tal)|7559]]
| [[7561 (tal)|7561]]
|-
! {{Nowrap|961 – 980}}
| [[7573 (tal)|7573]]
| [[7577 (tal)|7577]]
| [[7583 (tal)|7583]]
| [[7589 (tal)|7589]]
| [[7591 (tal)|7591]]
| [[7603 (tal)|7603]]
| [[7607 (tal)|7607]]
| [[7621 (tal)|7621]]
| [[7639 (tal)|7639]]
| [[7643 (tal)|7643]]
| [[7649 (tal)|7649]]
| [[7669 (tal)|7669]]
| [[7673 (tal)|7673]]
| [[7681 (tal)|7681]]
| [[7687 (tal)|7687]]
| [[7691 (tal)|7691]]
| [[7699 (tal)|7699]]
| [[7703 (tal)|7703]]
| [[7717 (tal)|7717]]
| [[7723 (tal)|7723]]
|-
! {{Nowrap|981 – 1 000}}
| [[7727 (tal)|7727]]
| [[7741 (tal)|7741]]
| [[7753 (tal)|7753]]
| [[7757 (tal)|7757]]
| [[7759 (tal)|7759]]
| [[7789 (tal)|7789]]
| [[7793 (tal)|7793]]
| [[7817 (tal)|7817]]
| [[7823 (tal)|7823]]
| [[7829 (tal)|7829]]
| [[7841 (tal)|7841]]
| [[7853 (tal)|7853]]
| [[7867 (tal)|7867]]
| [[7873 (tal)|7873]]
| [[7877 (tal)|7877]]
| [[7879 (tal)|7879]]
| [[7883 (tal)|7883]]
| [[7901 (tal)|7901]]
| [[7907 (tal)|7907]]
| [[7919 (tal)|7919]]
|}

Verifieringsprojektet av [[Goldbachs hypotes]] rapporterar att de har beräknat alla primtal under 4 × 10<sup>18</sup>,<ref>{{Webbref|titel=Goldbach conjecture verification|url=http://sweet.ua.pt/tos/goldbach.html|hämtdatum=14 augusti 2020|datum=30 december 2015|utgivare=[[Universitetet i Aveiro]]|efternamn=Oliveira e Silva|förnamn=Tomás|verk=Goldbach conjecture verification|språk=engelska|arkivurl=https://archive.today/20200814060945/http://sweet.ua.pt/tos/goldbach.html|arkivdatum=14 August 2020|författarlänk=Tomás Oliveira e Silva}}</ref> det vill säga {{Nowrap|95 676 260 903 887 607}} stycken. Dessa har dock inte lagrats i någon databas. Med [[primtalsfunktionen]] kan antalet primtal under ett visst värde uppskattas snabbare än vad det gör att faktiskt beräkna de med en dator. Den har använts för att beräkna att det finns {{Nowrap|1 925 320 391 606 803 968 923}} primtal under 10<sup>23</sup>. En annan beräkning fann att det finns {{Nowrap|18 435 599 767 349 200 867 866}} primtal under 10<sup>24</sup>, om [[Riemannhypotesen]] stämmer.<ref>{{Webbref|url=https://primes.utm.edu/notes/pi(10to24).html|titel=Conditional Calculation of π(10²⁴)|hämtdatum=14 augusti 2020|datum=|utgivare=PrimePages|språk=engelska|arkivurl=https://archive.today/20200814083649/https://primes.utm.edu/notes/pi(10to24).html|arkivdatum=2020-08-14|efternamn=Caldwell|förnamn=Chris|författarlänk=Chris K. Caldwell}}</ref>

== Listor över primtalsklasser ==

Nedan listas några klasser av primtal. Se i respektive artikel för mer information om varje klass. I varje form av primtal är <math display="inline">n\in \N_0</math> i definitionen.

=== Balanserat primtal ===

{{Huvudartikel|Balanserat primtal}}

Balanserade primtal är ett primtal på formen <math display="inline">p_n = {{p_{n - 1} + p_{n + 1}} \over 2}</math>, alltså att det [[Aritmetiskt medelvärde|aritmetiska medelvärdet]] av de närmaste primtalen före och efter, är lika med varandra.

{| class="wikitable mw-collapsible mw-collapsed" style="text-align: center; width: 100%;"
! colspan="21" | Tabell över de balanserande primtalen {{Ej fet|{{OEIS|A006562}}}}
|-
! {{Nowrap|1 – 20}}
| [[5 (tal)|5]]
| [[53 (tal)|53]]
| [[157 (tal)|157]]
| [[173 (tal)|173]]
| [[211 (tal)|211]]
| [[257 (tal)|257]]
| [[263 (tal)|263]]
| [[373 (tal)|373]]
| [[563 (tal)|563]]
| [[593 (tal)|593]]
| [[607 (tal)|607]]
| [[653 (tal)|653]]
| [[733 (tal)|733]]
| [[947 (tal)|947]]
| [[977 (tal)|977]]
| [[1103 (tal)|1103]]
| [[1123 (tal)|1123]]
| [[1187 (tal)|1187]]
| [[1223 (tal)|1223]]
| [[1367 (tal)|1367]]
|- 
! {{Nowrap|21 – 40}}
| [[1511 (tal)|1511]]
| [[1747 (tal)|1747]]
| [[1753 (tal)|1753]]
| [[1907 (tal)|1907]]
| [[2287 (tal)|2287]]
| [[2417 (tal)|2417]]
| [[2677 (tal)|2677]]
| [[2903 (tal)|2903]]
| [[2963 (tal)|2963]]
| [[3307 (tal)|3307]]
| [[3313 (tal)|3313]]
| [[3637 (tal)|3637]]
| [[3733 (tal)|3733]]
| [[4013 (tal)|4013]]
| [[4409 (tal)|4409]]
| [[4457 (tal)|4457]]
| [[4597 (tal)|4597]]
| [[4657 (tal)|4657]]
| [[4691 (tal)|4691]]
| [[4993 (tal)|4993]]
|}

=== Carolprimtal ===

{{Huvudartikel|Carolprimtal}}

Ett carolprimtal är ett [[caroltal]] som även är ett primtal och är på formen <math display="inline">p_n=(2^n - 1)^2 - 2</math>.

{| class="wikitable mw-collapsible mw-collapsed" style="text-align: center; width: 100%;"
! colspan="21" | Tabell över carolprimtalen {{Ej fet|{{OEIS|A091516}}}}
|-
! {{Nowrap|1 – 14}}
| [[7 (tal)|7]]
| [[47 (tal)|47]]
| [[223 (tal)|223]]
| [[3967 (tal)|3967]]
| [[16127 (tal)|16127]]
| [[1046527 (tal)|1046527]]
| [[16769023 (tal)|16769023]]
| [[1073676287 (tal)|1073676287]]
| [[68718952447 (tal)|68718952447]]
| [[274876858367 (tal)|274876858367]]
| [[4398042316799 (tal)|4398042316799]]
| [[1125899839733759 (tal)|1125899839733759]]
| [[18014398241046527 (tal)|18014398241046527]]
| [[1298074214633706835075030044377087 (tal)|1298074214633706835075030044377087]]
|}

=== Chenprimtal ===

{{Huvudartikel|Chenprimtal}}

Chenprimtal är ett primtal <math display="inline">p</math> där <math display="inline">p + 2</math> är antingen ett primtal eller ett [[semiprimtal]].

{| class="wikitable mw-collapsible mw-collapsed" style="text-align: center; width: 100%;"
! colspan="21" | Tabell över chenprimtalen {{Ej fet|{{OEIS|A068652}}}}
|-
! {{Nowrap|1 – 20}}
| [[2 (tal)|2]]
| [[3 (tal)|3]]
| [[5 (tal)|5]]
| [[7 (tal)|7]]
| [[11 (tal)|11]]
| [[13 (tal)|13]]
| [[17 (tal)|17]]
| [[19 (tal)|19]]
| [[23 (tal)|23]]
| [[29 (tal)|29]]
| [[31 (tal)|31]]
| [[37 (tal)|37]]
| [[41 (tal)|41]]
| [[47 (tal)|47]]
| [[53 (tal)|53]]
| [[59 (tal)|59]]
| [[67 (tal)|67]]
| [[71 (tal)|71]]
| [[83 (tal)|89]]
| [[101 (tal)|101]]
|-
! {{Nowrap|21 – 40}}
| [[107 (tal)|107]]
| [[109 (tal)|109]]
| [[113 (tal)|113]]
| [[127 (tal)|127]]
| [[131 (tal)|131]]
| [[137 (tal)|137]]
| [[139 (tal)|139]]
| [[149 (tal)|149]]
| [[157 (tal)|157]]
| [[167 (tal)|167]]
| [[179 (tal)|179]]
| [[181 (tal)|181]]
| [[191 (tal)|191]]
| [[197 (tal)|197]]
| [[199 (tal)|199]]
| [[211 (tal)|211]]
| [[227 (tal)|227]]
| [[233 (tal)|233]]
| [[239 (tal)|239]]
| [[251 (tal)|251]]
|-
! {{Nowrap|41 – 57}}
| [[257 (tal)|257]]
| [[263 (tal)|263]]
| [[269 (tal)|269]]
| [[281 (tal)|281]]
| [[293 (tal)|293]]
| [[307 (tal)|307]]
| [[311 (tal)|311]]
| [[317 (tal)|317]]
| [[337 (tal)|337]]
| [[347 (tal)|347]]
| [[353 (tal)|353]]
| [[359 (tal)|359]]
| [[379 (tal)|379]]
| [[389 (tal)|389]]
| [[401 (tal)|401]]
| [[409 (tal)|409]]
| <!-- FYLL GÄRNA I DE SAKNADE PRIMTALEN -->
| <!-- FYLL GÄRNA I DE SAKNADE PRIMTALEN -->
| <!-- FYLL GÄRNA I DE SAKNADE PRIMTALEN -->
| <!-- FYLL GÄRNA I DE SAKNADE PRIMTALEN -->
|}

=== Fermatprimtal ===

{{Huvudartikel|Fermatprimtal}}

Ett fermatprimtal är ett [[fermattal]] som även är ett primtal på formen <math display="inline">F_{n} = 2^{2^n} + 1</math>.

{| class="wikitable mw-collapsible mw-collapsed" style="text-align: center; width: 100%;"
! colspan="21" | Tabell över fermatprimtalen {{Ej fet|{{OEIS|A019434}}}}
|-
! {{Nowrap|1 – 5}}
| [[3 (tal)|3]]
| [[5 (tal)|5]]
| [[17 (tal)|17]]
| [[257 (tal)|257]]
| [[65537 (tal)|65537]]
|}

I tabellen ovan anges dem enda kända fermatprimtalen. Sannolikheten för att det finns fler fermatprimtal är mindre än en av en miljard.<ref>{{Tidskriftsref|rubrik=Expect at Most One Billionth of a New Fermat Prime!|efternamn=Boklan|författarlänk2=John Horton Conway|utgivningsort=New York|oclc=6925778794|id=[[arXiv]]:[https://arxiv.org/abs/1605.01371 1605.01371]|utgivare=[[Springer Journals]]|datum=11 januari 2017|efternamn2=Conway|förnamn2=John|förnamn=Kent|url=https://arxiv.org/pdf/1605.01371.pdf|språk=engelska|doi=10.1007/s00283-016-9644-3|nummer=1|volym=39|sid=3–5|issn=0343-6993|hämtdatum=15 augusti 2020|tidskrift=[[The Mathematical Intelligencer]]|författarlänk=Kent Boklan}}</ref>

=== Mersenneprimtal ===

{{Huvudartikel|Mersenneprimtal}}

Ett mersenneprimtal är ett [[mersennetal]] som även är ett primtal på formen <math display="inline">p_{n} = {2^n} - 1</math>.

{| class="wikitable mw-collapsible mw-collapsed" style="text-align: center; width: 100%;"
! colspan="21" | Tabell över mersenneprimtalen {{Ej fet|{{OEIS|A000668}}}}
|-
! {{Nowrap|1 – 12}}
| [[3 (tal)|3]]
| [[7 (tal)|7]]
| [[31 (tal)|31]]
| [[127 (tal)|127]]
| [[8191 (tal)|8191]]
| [[131071 (tal)|131071]]
| [[524287 (tal)|524287]]
| [[2147483647 (tal)|2147483647]]
| [[2305843009213693951 (tal)|2305843009213693951]]
| [[618970019642690137449562111 (tal)|618970019642690137449562111]]
| [[162259276829213363391578010288127 (tal)|162259276829213363391578010288127]]
| [[170141183460469231731687303715884105727 (tal)|170141183460469231731687303715884105727]]
|}

Det finns endast 51 stycken kända mersenneprimtal. Det [[Stora primtal|största kända primtalet]] är ett primtal av denna form och innehåller {{Nowrap|24 862 048}} siffror.<ref>{{Webbref|titel=51st Known Mersenne Prime Discovered|url=https://www.mersenne.org/primes/press/M82589933.html|hämtdatum=15 augusti 2020|datum=21 december 2018|utgivare=Mersenne Research|språk=engelska|arkivurl=https://archive.today/20200815183924/https://www.mersenne.org/primes/press/M82589933.html|arkivdatum=15 August 2020|verk=[[GIMPS]]}}</ref>

=== Mills primtal ===

{{Huvudartikel|Mills primtal}}

Mills primtal är ett primtal på formen <math display="inline">\lfloor \theta^{3^{n}} \rfloor</math> där <math display="inline">\theta</math> är [[Mills konstant]]. Det gäller för alla positiva [[heltal]] <math display="inline">n</math>.

{| class="wikitable mw-collapsible mw-collapsed" style="text-align: center; width: 100%;"
! colspan="21" | Tabell över Mills primtal {{Ej fet|{{OEIS|A051254}}}}
|-
! {{Nowrap|1 – 5}}
| [[2 (tal)|2]]
| [[11 (tal)|11]]
| [[1361 (tal)|1361]]
| [[2521008887 (tal)|2521008887]]
| [[16022236204009818131831320183 (tal)|16022236204009818131831320183]]
|}

=== Palindromprimtal ===

{{Huvudartikel|Palindromprimtal}}

Palindromprimtal är ett [[palindromtal]] som även är ett primtal.

{| class="wikitable mw-collapsible mw-collapsed" style="text-align: center; width: 100%;"
! colspan="21" | Tabell över palindromprimtalen {{Ej fet|{{OEIS|A002385}}}}
|-
! {{Nowrap|1 – 20}}
| [[2 (tal)|2]]
| [[3 (tal)|3]]
| [[5 (tal)|5]]
| [[7 (tal)|7]]
| [[11 (tal)|11]]
| [[101 (tal)|101]]
| [[131 (tal)|131]]
| [[151 (tal)|151]]
| [[181 (tal)|181]]
| [[191 (tal)|191]]
| [[313 (tal)|313]]
| [[353 (tal)|353]]
| [[373 (tal)|373]]
| [[383 (tal)|383]]
| [[727 (tal)|727]]
| [[757 (tal)|757]]
| [[787 (tal)|787]]
| [[797 (tal)|797]]
| [[919 (tal)|919]]
| [[929 (tal)|929]]
|-
! {{Nowrap|21 – 40}}
| [[10301 (tal)|10301]]
| [[10501 (tal)|10501]]
| [[10601 (tal)|10601]]
| [[11311 (tal)|11311]]
| [[11411 (tal)|11411]]
| [[12421 (tal)|12421]]
| [[12721 (tal)|12721]]
| [[12821 (tal)|12821]]
| [[13331 (tal)|13331]]
| [[13831 (tal)|13831]]
| [[13931 (tal)|13931]]
| [[14341 (tal)|14341]]
| [[14741 (tal)|14741]]
| [[15451 (tal)|15451]]
| [[15551 (tal)|15551]]
| [[16061 (tal)|16061]]
| [[16361 (tal)|16361]]
| [[16561 (tal)|16561]]
| [[16661 (tal)|16661]]
| [[17471 (tal)|17471]]
|}

== Se även ==
* [[Stora primtal]]
* [[Lista över tal]]
* [[Primtalssatsen]]
* [[Pseudoprimtal]]

== Referenser ==

=== Anmärkningar ===

{{Anmärkningslista}}

=== Källor ===

<references/>

== Externa länkar ==

* [https://primes.utm.edu/lists/ Listor över primtal] på PrimePages
* [http://www.prime-numbers.org/ Full lista över primtalen] under {{Nowrap|10 000 000 000}} på Prime-Numbers.org
* [https://mathworld.wolfram.com/topics/PrimeNumberSequences.html Primtalsföljder] på [[MathWorld]] av [[Eric W. Weisstein]]
* [http://oeis.org/wiki/Index_to_OEIS:_Section_Pri Utvalda primtalsföjder] på [[OEIS]]
* [https://www.youtube.com/playlist?list=PL0D0BD149128BB06F Spellista om primtal] på [[YouTube]] av [[Numberphile]]

{{Primtal}}

[[Kategori:Primtal]]
[[Kategori:Primtalsklasser|Primtal]]
[[Kategori:Listor med anknytning till matematik|Primtal]]