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((Navbox
|name = Prime number classes
|title = [[Prime number]] classes
|listclass = hlist
|state = (({state|autocollapse))}

|group1 = By formula
|list1 = 
* [[Fermat number|Fermat (((math|size=110%|1=2<sup>2<sup>''n''</sup></sup>&nbsp;+&nbsp;1)))]]
* [[Mersenne prime|Mersenne (((math|size=110%|1=2<sup>''p''</sup>&nbsp;−&nbsp;1)))]]
* [[Double Mersenne number|Double Mersenne (((math|size=110%|1=2<sup>2<sup>''p''</sup>−1</sup>&nbsp;−&nbsp;1)))]]
* [[Wagstaff prime|Wagstaff  ((math|size=110%|1=(2<sup>''p''</sup>&nbsp;+&nbsp;1)/3))]]
* [[Proth prime|Proth (((math|size=110%|1=''k''·2<sup>''n''</sup>&nbsp;+&nbsp;1)))]]
* [[Factorial prime|Factorial (((math|size=110%|1=''n''!&nbsp;±&nbsp;1)))]]
* [[Primorial prime|Primorial (((math|size=110%|1=''p<sub>n</sub>''#&nbsp;±&nbsp;1)))]]
* [[Euclid number|Euclid (((math|size=110%|1=''p<sub>n</sub>''#&nbsp;+&nbsp;1)))]]
* [[Pythagorean prime|Pythagorean (((math|size=110%|1=4''n''&nbsp;+&nbsp;1)))]]
* [[Pierpont prime|Pierpont (((math|size=110%|1=2<sup>''m''</sup>·3<sup>''n''</sup>&nbsp;+&nbsp;1)))]]
* [[Quartan prime|Quartan (((math|size=110%|1=''x''<sup>4</sup>&nbsp;+&nbsp;''y''<sup>4</sup>)))]]
* [[Solinas prime|Solinas (((math|size=110%|1=2<sup>''m''</sup>&nbsp;±&nbsp;2<sup>''n''</sup>&nbsp;±&nbsp;1)))]]
* [[Cullen number|Cullen (((math|size=110%|1=''n''·2<sup>''n''</sup>&nbsp;+&nbsp;1)))]]
* [[Woodall number|Woodall (((math|size=110%|1=''n''·2<sup>''n''</sup>&nbsp;−&nbsp;1)))]]
* [[Cuban prime|Cuban (((math|size=110%|1=''x''<sup>3</sup>&nbsp;−&nbsp;''y''<sup>3</sup>)/(''x''&nbsp;−&nbsp;''y'')))]]
* [[Leyland number|Leyland (((math|size=110%|1=''x<sup>y</sup>''&nbsp;+&nbsp;''y<sup>x</sup>'')))]]
* [[Thabit number|Thabit (((math|size=110%|1=3·2<sup>''n''</sup>&nbsp;−&nbsp;1)))]]
* [[Williams number|Williams (((math|size=110%|1=(''b''−1)·''b''<sup>''n''</sup>&nbsp;−&nbsp;1)))]]
* [[Mills' constant|Mills (((math|size=110%|1=((floor|''A''<sup>3<sup>''n''</sup></sup>)))))]]

|group2 = By integer sequence
|list2 = 
* [[Fibonacci prime|Fibonacci]]
* [[Lucas prime|Lucas]]
* [[Pell prime|Pell]]
* [[Newman–Shanks–Williams prime|Newman–Shanks–Williams]]
* [[Perrin prime|Perrin]]

|group3 = By property
|list3 = 
* [[Wieferich prime|Wieferich]] ([[Wieferich pair|pair]])
* [[Wall–Sun–Sun prime|Wall–Sun–Sun]]
* [[Wolstenholme prime|Wolstenholme]]
* [[Wilson prime|Wilson]]
* [[Lucky number|Lucky]]
* [[Fortunate number|Fortunate]]
* [[Ramanujan prime|Ramanujan]]
* [[Pillai prime|Pillai]]
* [[Regular prime|Regular]]
* [[Strong prime|Strong]]
* [[Stern prime|Stern]]
* [[Supersingular prime (algebraic number theory)|Supersingular (elliptic curve)]]
* [[Supersingular prime (moonshine theory)|Supersingular (moonshine theory)]]
* [[Good prime|Good]]
* [[Super-prime|Super]]
* [[Higgs prime|Higgs]]
* [[Highly cototient number|Highly cototient]]
* [[Reciprocals of primes#Unique primes|Unique]]

|group4 = [[Radix|Base]]-dependent
|list4 = 
* [[Palindromic prime|Palindromic]]
* [[Emirp]]
* [[Repunit|Repunit ((math|size=110%|1=(10<sup>''n''</sup>&nbsp;−&nbsp;1)/9))]]
* [[Permutable prime|Permutable]]
* [[Circular prime|Circular]]
* [[Truncatable prime|Truncatable]]
* [[Minimal prime (recreational mathematics)|Minimal]]
* [[Delicate prime|Delicate]]
* [[Primeval number|Primeval]]
* [[Full reptend prime|Full reptend]]
* [[Unique prime number|Unique]]
* [[Happy number#Happy primes|Happy]]
* [[Self number|Self]]
* [[Smarandache–Wellin prime|Smarandache–Wellin]]
* [[Strobogrammatic prime|Strobogrammatic]]
* [[Dihedral prime|Dihedral]]
* [[Tetradic number|Tetradic]]

|group5 = Patterns
|list5 = 
* [[Twin prime|Twin (((math|size=110%|1=''p'', ''p''&nbsp;+&nbsp;2)))]]
* [[Bi-twin chain|Bi-twin chain (((math|size=110%|1=''n''&nbsp;±&nbsp;1, 2''n''&nbsp;±&nbsp;1, 4''n''&nbsp;±&nbsp;1, …)))]]
* [[Prime triplet|Triplet (((math|size=110%|1=''p'', ''p''&nbsp;+&nbsp;2 or ''p''&nbsp;+&nbsp;4, ''p''&nbsp;+&nbsp;6)))]]
* [[Prime quadruplet|Quadruplet (((math|size=110%|1=''p'', ''p''&nbsp;+&nbsp;2, ''p''&nbsp;+&nbsp;6, ''p''&nbsp;+&nbsp;8)))]]
* [[Prime k-tuple|''k''-tuple]]
* [[Cousin prime|Cousin (((math|size=110%|1=''p'', ''p''&nbsp;+&nbsp;4)))]]
* [[Sexy prime|Sexy (((math|size=110%|1=''p'', ''p''&nbsp;+&nbsp;6)))]]
* [[Chen prime|Chen]]
* [[Safe and Sophie Germain primes|Sophie Germain/Safe (((math|size=110%|1=''p'', 2''p''&nbsp;+&nbsp;1)))]]
* [[Cunningham chain|Cunningham (((math|size=110%|1=''p'', 2''p''&nbsp;±&nbsp;1, 4''p''&nbsp;±&nbsp;3, 8''p''&nbsp;±&nbsp;7, ...)))]]
* [[Primes in arithmetic progression|Arithmetic progression (((math|size=110%|1=''p''&nbsp;+&nbsp;''a·n'', ''n''&nbsp;=&nbsp;0,&nbsp;1,&nbsp;2,&nbsp;3,&nbsp;...)))]]
* [[Balanced prime|Balanced (((math|size=110%|1=consecutive ''p''&nbsp;−&nbsp;''n'', ''p'', ''p''&nbsp;+&nbsp;''n'')))]]

|group6 = By size
|list6 = 
* [[Megaprime|Mega (1,000,000+ digits)]]
* [[Largest known prime number|Largest known]]
** [[List of largest known primes and probable primes|list]]

|group7 = [[Complex number|Complex numbers]]
|list7 = 
* [[Eisenstein prime]]
* [[Gaussian integer#Gaussian primes|Gaussian prime]]

|group8 = [[Composite number|Composite numbers]]
|list8 = 
* [[Pseudoprime]]
** [[Catalan pseudoprime|Catalan]]
** [[Elliptic pseudoprime|Elliptic]]
** [[Euler pseudoprime|Euler]]
** [[Euler–Jacobi pseudoprime|Euler–Jacobi]]
** [[Fermat pseudoprime|Fermat]]
** [[Frobenius pseudoprime|Frobenius]]
** [[Lucas pseudoprime|Lucas]]
** [[Perrin pseudoprime|Perrin]]
** [[Somer–Lucas pseudoprime|Somer–Lucas]]
** [[Strong pseudoprime|Strong]]
* [[Carmichael number]]
* [[Almost prime]]
* [[Semiprime]]
* [[Sphenic number]]
* [[Interprime]]
* [[Pernicious number|Pernicious]]

|group9 = Related topics
|list9 = 
* [[Probable prime]]
* [[Industrial-grade prime]]
* [[Illegal prime]]
* [[Formula for primes]]
* [[Prime gap]]

|group10 = First ((#expr:60+(((CURRENTMONTH))((CURRENTDAY2))=401))) primes
|list10 =
((#ifeq:((CURRENTMONTH))((CURRENTDAY2))|401|* [[1]]))
* [[2]]
* [[3]]
* [[5]]
* [[7]]
* [[11 (number)|11]]
* [[13 (number)|13]]
* [[17 (number)|17]]
* [[19 (number)|19]]
* [[23 (number)|23]]
* [[29 (number)|29]]
* [[31 (number)|31]]
* [[37 (number)|37]]
* [[41 (number)|41]]
* [[43 (number)|43]]
* [[47 (number)|47]]
* [[53 (number)|53]]
* [[59 (number)|59]]
* [[61 (number)|61]]
* [[67 (number)|67]]
* [[71 (number)|71]]
* [[73 (number)|73]]
* [[79 (number)|79]]
* [[83 (number)|83]]
* [[89 (number)|89]]
* [[97 (number)|97]]
* [[101 (number)|101]]
* [[103 (number)|103]]
* [[107 (number)|107]]
* [[109 (number)|109]]
* [[113 (number)|113]]
* [[127 (number)|127]]
* [[131 (number)|131]]
* [[137 (number)|137]]
* [[139 (number)|139]]
* [[149 (number)|149]]
* [[151 (number)|151]]
* [[157 (number)|157]]
* [[163 (number)|163]]
* [[167 (number)|167]]
* [[173 (number)|173]]
* [[179 (number)|179]]
* [[181 (number)|181]]
* [[191 (number)|191]]
* [[193 (number)|193]]
* [[197 (number)|197]]
* [[199 (number)|199]]
* [[211 (number)|211]]
* [[223 (number)|223]]
* [[227 (number)|227]]
* [[229 (number)|229]]
* [[233 (number)|233]]
* [[239 (number)|239]]
* [[241 (number)|241]]
* [[251 (number)|251]]
* [[257 (number)|257]]
* [[263 (number)|263]]
* [[269 (number)|269]]
* [[271 (number)|271]]
* [[277 (number)|277]]
* [[281 (number)|281]]

| belowclass = hlist
| below = 
[[List of prime numbers]]

))<noinclude>
((documentation|content=

((collapsible option))

==See also==
*((tl|Classes of natural numbers))
*((tl|Series (mathematics)))

[[Category:Mathematics navigational boxes]]
))
</noinclude>

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