Pseudoprimo: diferenças entre revisões

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Nuno Tavares (discussão | contribs)
m #REDIRECT Pseudoprimalidade
 
esboço
Linha 1:
Um '''pseudoprimo''' is um [[primo provável]] (um [[intiro]] que compartilha a propriedade comum dos [[número primo|números primos]]) que na verdade não é primo. Pseudoprimos podem ser classificados de acordo com a propriedade que eles satisfazem.
#REDIRECT [[Pseudoprimalidade]]
 
 
{| {{prettytable}}
|n || ||n || ||n || ||n || ||n ||
|-
|1 ||341 = 11 · 31 ||11 ||'''2821''' = 7 · 13 · 31 ||21 ||8481 = 3 · 11 · 257 ||31 ||15709 = 23 · 683 ||41 ||30121 = 7 · 13 · 331
|-
|2 ||'''561''' = 3 · 11 · 17 ||12 ||3277 = 29 · 112 ||22 ||'''8911''' = 7 · 19 · 67 ||32 ||'''15841''' = 7 · 31 · 73 ||42 ||30889 = 17 · 23 · 79
|-
|3 ||645 = 3 · 5 · 43 ||13 ||4033 = 37 · 109 ||23 ||10261 = 31 · 331 ||33 ||16705 = 5 · 13 · 257 ||43 ||31417 = 89 · 353
|-
|4 ||'''1105''' = 5 · 13 · 17 ||14 ||4369 = 17 · 257 ||24 ||'''10585''' = 5 · 29 · 73 ||34 ||18705 = 3 · 5 · 29 · 43 ||44 ||31609 = 73 · 433
|-
|5 ||1387 = 19 · 73 ||15 ||4371 = 3 · 31 · 47 ||25 ||11305 = 5 · 7 · 17 · 19 ||35 ||18721 = 97 · 193 ||45 ||31621 = 103 · 307
|-
|6 ||'''1729''' = 7 · 13 · 19 ||16 ||4681 = 31 · 151 ||26 ||12801 = 3 · 17 · 251 ||36 ||19951 = 71 · 281 ||46 ||33153 = 3 · 43 · 257
|-
|7 ||1905 = 3 · 5 · 127 ||17 ||5461 = 43 · 127 ||27 ||13741 = 7 · 13 · 151 ||37 ||23001 = 3 · 11 · 17 · 41 ||47 ||34945 = 5 · 29 · 241
|-
|8 ||2047 = 23 · 89 ||18 ||'''6601''' = 7 · 23 · 41 ||28 ||13747 = 59 · 233 ||38 ||23377 = 97 · 241 ||48 ||35333 = 89 · 397
|-
|9 ||'''2465''' = 5 · 17 · 29 ||19 ||7957 = 73 · 109 ||29 ||13981 = 11 · 31 · 41 ||39 ||25761 = 3 · 31 · 277 ||49 ||39865 = 5 · 7 · 17 · 67
|-
|10 ||2701 = 37 · 73 ||20 ||8321 = 53 · 157 ||30 ||14491 = 43 · 337 ||40 ||'''29341''' = 13 · 37 · 61 ||50 ||'''41041''' = 7 · 11 · 13 · 41
|}
 
A Poulet number all of whose divisors ''d'' divide 2<sup>''d''</sup> - 2 is called
[[super-Poulet number]]. There are an infinitely many Poulet numbers which are not super-Poulet Numbers.
 
The first smallest pseudoprimes for bases ''a'' &le; 200 are given in the following table; the colors mark the number of prime factors.
 
{| {{prettytable}}
|-
! ''a''
! smallest p-p
! ''a''
! smallest p-p
! ''a''
! smallest p-p
! ''a''
! smallest p-p
|-
| &nbsp;
| &nbsp;
| 51
| 65 = 5 &middot; 13
| bgcolor="#FFEBAD" | 101
| bgcolor="#FFEBAD" | 175 = 5<sup>2</sup> &middot; 7
| bgcolor="#FFEBAD" | 151
| bgcolor="#FFEBAD" | 175 = 5<sup>2</sup> &middot; 7
|-
| 2
| 341 = 11 &middot; 13
| 52
| 85 = 5 &middot; 17
| 102
| 133 = 7 &middot; 19
| bgcolor="#FFEBAD" | 152
| bgcolor="#FFEBAD" | 153 = 3<sup>2</sup> &middot; 17
|-
| 3
| 91 = 7 &middot; 13
| 53
| 65 = 5 &middot; 13
| 103
| 133 = 7 &middot; 19
| 153
| 209 = 11 &middot; 19
|-
| 4
| 15 = 3 &middot; 5
| 54
| 55 = 5 &middot; 11
| bgcolor="#B3B7FF" | 104
| bgcolor="#B3B7FF" | 105 = 3 &middot; 5 &middot; 7
| 154
| 155 = 5 &middot; 31
|-
| bgcolor="#FFEBAD" | 5
| bgcolor="#FFEBAD" | 124 = 2<sup>2</sup> &middot; 31
| bgcolor="#FFEBAD" | 55
| bgcolor="#FFEBAD" | 63 = 3<sup>2</sup> &middot; 7
| 105
| 451 = 11 &middot; 41
| bgcolor="#B3B7FF" | 155
| bgcolor="#B3B7FF" | 231 = 3 &middot; 7 &middot; 11
|-
| 6
| 35 = 5 &middot; 7
| 56
| 57 = 3 &middot; 19
| 106
| 133 = 7 &middot; 19
| 156
| 217 = 7 &middot; 31
|-
| bgcolor="#FFCBCB" | 7
| bgcolor="#FFCBCB" | 25 = 5<sup>2</sup>
| 57
| 65 = 5 &middot; 13
| 107
| 133 = 7 &middot; 19
| bgcolor="#B3B7FF" | 157
| bgcolor="#B3B7FF" | 186 = 2 &middot; 3 &middot; 31
|-
| bgcolor="#FFCBCB" | 8
| bgcolor="#FFCBCB" | 9 = 3<sup>2</sup>
| 58
| 133 = 7 &middot; 19
| 108
| 341 = 11 &middot; 31
| 158
| 159 = 3 &middot; 53
|-
| bgcolor="#FFEBAD" | 9
| bgcolor="#FFEBAD" | 28 = 2<sup>2</sup> &middot; 7
| 59
| 87 = 3 &middot; 29
| bgcolor="#FFEBAD" | 109
| bgcolor="#FFEBAD" | 117 = 3<sup>2</sup> &middot; 13
| 159
| 247 = 13 &middot; 19
|-
| 10
| 33 = 3 &middot; 11
| 60
| 341 = 11 &middot; 31
| 110
| 111 = 3 &middot; 37
| 160
| 161 = 7 &middot; 23
|-
| 11
| 15 = 3 &middot; 5
| 61
| 91 = 7 &middot; 13
| bgcolor="#B3B7FF" | 111
| bgcolor="#B3B7FF" | 190 = 2 &middot; 5 &middot; 19
| bgcolor="#B3B7FF" | 161
| bgcolor="#B3B7FF" | 190=2 &middot; 5 &middot; 19
|-
| 12
| 65 = 5 &middot; 13
| bgcolor="#FFEBAD" | 62
| bgcolor="#FFEBAD" | 63 = 3<sup>2</sup> &middot; 7
| bgcolor="#FFCBCB" | 112
| bgcolor="#FFCBCB" | 121 = 11<sup>2</sup>
| 162
| 481 = 13 &middot; 37
|-
| 13
| 21 = 3 &middot; 7
| 63
| 341 = 11 &middot; 31
| 113
| 133 = 7 &middot; 19
| bgcolor="#B3B7FF" | 163
| bgcolor="#B3B7FF" | 186 = 2 &middot; 3 &middot; 31
|-
| 14
| 15 = 3 &middot; 5
| 64
| 65 = 5 &middot; 13
| 114
| 115 = 5 &middot; 23
| bgcolor="#B3B7FF" | 164
| bgcolor="#B3B7FF" | 165 = 3 &middot; 5 &middot; 11
|-
| 15
| 341 = 11 · 13
| bgcolor="#FFEBAD" | 65
| bgcolor="#FFEBAD" | 112 = 2<sup>4</sup> &middot; 7
| 115
| 133 = 7 &middot; 19
| bgcolor="#FFEBAD" | 165
| bgcolor="#FFEBAD" | 172 = 2<sup>2</sup> &middot; 43
|-
| 16
| 51 = 3 &middot; 17
| 66
| 91 = 7 &middot; 13
| bgcolor="#FFEBAD" | 116
| bgcolor="#FFEBAD" | 117 = 3<sup>2</sup> &middot; 13
| 166
| 301 = 7 &middot; 43
|-
| bgcolor="#FFEBAD" | 17
| bgcolor="#FFEBAD" | 45 = 3<sup>2</sup> &middot; 5
| 67
| 85 = 5 &middot; 17
| 117
| 145 = 5 &middot; 29
| bgcolor="#B3B7FF" | 167
| bgcolor="#B3B7FF" | 231 = 3 &middot; 7 &middot; 11
|-
| bgcolor="#FFCBCB" | 18
| bgcolor="#FFCBCB" | 25 = 5<sup>2</sup>
| 68
| 69 = 3 &middot; 23
| 118
| 119 = 7 &middot; 17
| bgcolor="#FFCBCB" | 168
| bgcolor="#FFCBCB" | 169 = 13<sup>2</sup>
|-
| bgcolor="#FFEBAD" | 19
| bgcolor="#FFEBAD" | 45 = 3<sup>2</sup> &middot; 5
| 69
| 85 = 5 &middot; 17
| 119
| 177 = 3 &middot; 59
| bgcolor="#B3B7FF" | 169
| bgcolor="#B3B7FF" | 231 = 3 &middot; 7 &middot; 11
|-
| 20
| 21 = 3 &middot; 7
| bgcolor="#FFCBCB" | 70
| bgcolor="#FFCBCB" | 169 = 13<sup>2</sup>
| bgcolor="#FFCBCB" | 120
| bgcolor="#FFCBCB" | 121 = 11<sup>2</sup>
| bgcolor="#FFEBAD" | 170
| bgcolor="#FFEBAD" | 171 = 3<sup>2</sup> &middot; 19
|-
| 21
| 55 = 5 &middot; 11
| bgcolor="#B3B7FF" | 71
| bgcolor="#B3B7FF" | 105 = 3 &middot; 5 &middot; 7
| 121
| 133 = 7 &middot; 19
| 171
| 215 = 5 &middot; 43
|-
| 22
| 69 = 3 &middot; 23
| 72
| 85 = 5 &middot; 17
| 122
| 123 = 3 &middot; 41
| 172
| 247 = 13 &middot; 19
|-
| 23
| 33 = 3 &middot; 11
| 73
| 111 = 3 &middot; 37
| 123
| 217 = 7 &middot; 31
| 173
| 205 = 5 &middot; 41
|-
| bgcolor="#FFCBCB" | 24
| bgcolor="#FFCBCB" | 25 = 5<sup>2</sup>
| bgcolor="#FFEBAD" | 74
| bgcolor="#FFEBAD" | 75 = 3 &middot; 5<sup>2</sup>
| bgcolor="#FFEBAD" | 124
| bgcolor="#FFEBAD" | 125 = 3<sup>3</sup>
| bgcolor="#FFEBAD" | 174
| bgcolor="#FFEBAD" | 175 = 5<sup>2</sup> &middot; 7
|-
| bgcolor="#FFEBAD" | 25
| bgcolor="#FFEBAD" | 28 = 2<sup>2</sup> &middot; 7
| 75
| 91 = 7 &middot; 13
| 125
| 133 = 7 &middot; 19
| 175
| 319 = 11 &middot; 19
|-
| bgcolor="#FFEBAD" | 26
| bgcolor="#FFEBAD" | 27 = 3<sup>3</sup>
| 76
| 77 = 7 &middot; 11
| 126
| 247 = 13 &middot; 19
| 176
| 177 = 3 &middot; 59
|-
| 27
| 65 = 5 &middot; 13
| 77
| 247 = 13 &middot; 19
| bgcolor="#FFEBAD" | 127
| bgcolor="#FFEBAD" | 153 = 3<sup>2</sup> &middot; 17
| bgcolor="#FFEBAD" | 177
| bgcolor="#FFEBAD" | 196 = 2<sup>2</sup> &middot; 7<sup>2</sup>
|-
| bgcolor="#FFEBAD" | 28
| bgcolor="#FFEBAD" | 45 = 3<sup>2</sup> &middot; 5
| 78
| 341 = 11 &middot; 31
| 128
| 129 = 3 &middot; 43
| 178
| 247 = 13 &middot; 19
|-
| 29
| 35 = 5 &middot; 7
| 79
| 91 = 7 &middot; 13
| 129
| 217 = 7 &middot; 31
| 179
| 185 = 5 &middot; 37
|-
| bgcolor="#FFCBCB" | 30
| bgcolor="#FFCBCB" | 49 = 7<sup>2</sup>
| bgcolor="#FFEBAD" | 80
| bgcolor="#FFEBAD" | 81 = 3<sup>4</sup>
| 130
| 217 = 7 &middot; 31
| 180
| 217 = 7 &middot; 31
|-
| bgcolor="#FFCBCB" | 31
| bgcolor="#FFCBCB" | 49 = 7<sup>2</sup>
| 81 = 3<sup>4</sup>
| 85 = 5 &middot; 17
| 131
| 143 = 11 &middot; 13
| bgcolor="#B3B7FF" | 181
| bgcolor="#B3B7FF" | 195 = 3 &middot; 5 &middot; 13
|-
| 32
| 33 = 3 &middot; 11
| 82
| 91 = 7 &middot; 13
| 132
| 133 = 7 &middot; 19
| 182
| 183 = 3 &middot; 61
|-
| 33
| 85 = 5 &middot; 17
| bgcolor="#B3B7FF" | 83
| bgcolor="#B3B7FF" | 105 = 3 &middot; 5 &middot; 7
| 133
| 145 = 5 &middot; 29
| 183
| 221 = 13 &middot; 17
|-
| 34
| 35 = 5 &middot; 7
| 84
| 85 = 5 &middot; 17
| bgcolor="#FFEBAD" | 134
| bgcolor="#FFEBAD" | 135 = 3<sup>3</sup> &middot; 5
| 184
| 185 = 5 &middot; 37
|-
| 35
| 51 = 3 &middot; 17
| 85
| 129 = 3 &middot; 43
| 135
| 221 = 13 &middot; 17
| 185
| 217 = 7 &middot; 31
|-
| 36
| 91 = 7 &middot; 13
| 86
| 87 = 3 &middot; 29
| 136
| 265 = 5 &middot; 53
| 186
| 187 = 11 &middot; 17
|-
| bgcolor="#FFEBAD" | 37
| bgcolor="#FFEBAD" | 45 = 3<sup>2</sup> &middot; 5
| 87
| 91 = 7 &middot; 13
| bgcolor="#FFEBAD" | 137
| bgcolor="#FFEBAD" | 148 = 2<sup>2</sup> &middot; 37
| 187
| 217 = 7 &middot; 31
|-
| 38
| 39 = 3 &middot; 13
| 88
| 91 = 7 &middot; 13
| 138
| 259 = 7 &middot; 37
| bgcolor="#FFEBAD" | 188
| bgcolor="#FFEBAD" | 189 = 3<sup>3</sup> &middot; 7
|-
| 39
| 95 = 5 &middot; 19
| bgcolor="#FFEBAD" | 89
| bgcolor="#FFEBAD" | 99 = 3<sup>2</sup> &middot; 11
| 139
| 161 = 7 &middot; 23
| 189
| 235 = 5 &middot; 47
|-
| 40
| 91 = 7 &middot; 13
| 90
| 91 = 7 &middot; 13
| 140
| 141 = 3 &middot; 47
| bgcolor="#B3B7FF" | 190
| bgcolor="#B3B7FF" | 231 = 3 &middot; 7 &middot; 11
|-
| bgcolor="#B3B7FF" | 41
| bgcolor="#B3B7FF" | 105 = 3 &middot; 5 &middot; 7
| 91
| 115 = 5 &middot; 23
| 141
| 355 = 5 &middot; 71
| 191
| 217 = 7 &middot; 31
|-
| 42
| 205 = 5 &middot; 41
| 92
| 93 = 3 &middot; 31
| 142
| 143 = 11 &middot; 13
| 192
| 217 = 7 &middot; 31
|-
| 43
| 77 = 7 &middot; 11
| 93
| 301 = 7 &middot; 43
| 143
| 213 = 3 &middot; 71
| bgcolor="#FFEBAD" | 193
| bgcolor="#FFEBAD" | 276 = 2<sup>2</sup> &middot; 3 &middot; 23
|-
| bgcolor="#FFEBAD" | 44
| bgcolor="#FFEBAD" | 45 = 3<sup>2</sup> &middot; 5
| 94
| 95 = 5 &middot; 19
| 144
| 145 = 5 &middot; 29
| bgcolor="#B3B7FF" | 194
| bgcolor="#B3B7FF" | 195 = 3 &middot; 5 &middot; 13
|-
| bgcolor="#FFEBAD" | 45
| bgcolor="#FFEBAD" | 76 = 2<sup>2</sup> &middot; 19
| 95
| 141 = 3 &middot; 47
| bgcolor="#FFEBAD" | 145
| bgcolor="#FFEBAD" | 153 = 3<sup>2</sup> &middot; 17
| 195
| 259 = 7 &middot; 37
|-
| 46
| 133 = 7 &middot; 19
| 96
| 133 = 7 &middot; 19
| bgcolor="#FFEBAD" | 146
| bgcolor="#FFEBAD" | 147 = 3 &middot; 7<sup>2</sup>
| 196
| 205 = 5 &middot; 41
|-
| 47
| 65 = 5 &middot; 13
| bgcolor="#B3B7FF" | 97
| bgcolor="#B3B7FF" | 105 = 3 &middot; 5 &middot; 7
| bgcolor="#FFCBCB" | 147
| bgcolor="#FFCBCB" | 169 = 13<sup>2</sup>
| bgcolor="#B3B7FF" | 197
| bgcolor="#B3B7FF" | 231 = 3 &middot; 7 &middot; 11
|-
| bgcolor="#FFCBCB" | 48
| bgcolor="#FFCBCB" | 49 = 7<sup>2</sup>
| bgcolor="#FFEBAD" | 98
| bgcolor="#FFEBAD" | 99 = 3<sup>2</sup> &middot; 11
| bgcolor="#B3B7FF" | 148
| bgcolor="#B3B7FF" | 231 = 3 &middot; 7 &middot; 11
| 198
| 247 = 13 &middot; 19
|-
| bgcolor="#B3B7FF" | 49
| bgcolor="#B3B7FF" | 66 = 2 &middot; 3 &middot; 11
| 99
| 145 = 5 &middot; 29
| bgcolor="#FFEBAD" | 149
| bgcolor="#FFEBAD" | 175 = 5<sup>2</sup> &middot; 7
| bgcolor="#FFEBAD" | 199
| bgcolor="#FFEBAD" | 225 = 3<sup>2</sup> &middot; 5<sup>2</sup>
|-
| 50
| 51 = 3 &middot; 17
| bgcolor="#FFEBAD" | 100
| bgcolor="#FFEBAD" | 153 = 3<sup>2</sup> &middot; 17
| bgcolor="#FFCBCB" | 150
| bgcolor="#FFCBCB" | 169 = 13<sup>2</sup>
| 200
| 201 = 3 &middot; 67
|}
 
== Links externos ==
*[http://wikisource.org/wiki/Pseudoprime_numbers Pseudoprimos acima de 15.999]
 
{{esboço-matemática}}
 
[[Categoria:Álgebra]]
[[Categoria:Números primos]]
[[Categoria:Criptografia]]
 
[[de:Pseudoprimzahl]]
[[en:Pseudoprime]]
[[fr:Nombre pseudopremier]]
[[it:Pseudoprimo]]
[[sl:psevdopra&#353;tevilo]]
[[zh:&#20266;&#32032;&#25968;]]