按基排序的广义Fermat素数

形式的质数b^(2^n个) + 1称为广义费马素数。这里我们列出了这些按基数排序的素数b.

指数n个
b=20, 1, 2, 3, 4, ...
b=4请参见下方b=2
b=60, 1, 2, ...
b=8不可能,因为8=2^3
b=100, 1, ...
b=120, ...
b=141, ...
b=16请参见下方b=2
b=180, ...
b=201, 2, ...
b=220, ...
b=241, 2, ...
b=261, ...
b=280, 2, ...
b=300, 5, ...
b=32不可能,因为32=2^5
b=342, ...
b=36请参见下方b=6
b=38...
b=400, 1, ...
b=420, ...
b=444, ...
b=460, 2, 9, ...
b=482, ...
b=50...
b=520, ...
b=541, 2, 5, ...
b=561, 2, ...
b=580, ...
b=600, ...
b=62...
b=64不可能,因为64=4^3
b=660, 1, ...
b=68...
b=700, ...
b=720, ...
b=741, 2, 4, ...
b=764, ...
b=780, ...
b=802, ...
b=820, 2, ...
b=841, ...
b=86...
b=880, 2, ...
b=901, 2, ...
b=92...
b=941, 4, ...
b=960, 5, ...
b=98...
b=100请参见下方b=10
b=1020, 6, ...
b=104...
b=1060, 2, ...
b=1080, ...
b=1101, ...
b=1120, 5, ...
b=1145, ...
b=1161, ...
b=1182, 3, ...
b=1201, 7, ...
b=122...
b=1241, ...
b=1260, 1, ...
b=128不可能,因为128=2^7
b=1300, 1, ...
b=1322, 3, 5, ...
b=1341, ...
b=1360, ...
b=1380, ...
b=1402, 3, ...
b=1422, ...
b=144请参见下方b=12
b=1461, ...
b=1480, ...
b=1500, 1, 11, ...
b=1523, ...
b=1542, ...
b=1560, 1, 4, 5, ...
b=1584, ...
b=1601, 2, ...
b=1620, 6, ...
b=1642, ...
b=1660, ...
b=168...
b=1701, ...
b=1720, ...
b=1742, ...
b=1761, 4, ...
b=1780, ...
b=1800, 1, 2, ...
b=182...
b=1841, ...
b=186...
b=1884, ...
b=1900, 7, ...
b=1920, ...
b=1942, ...
b=196请参见下方b=14
b=1980, 2, 4, ...
b=200...
b=202...
b=2041, 2, ...
b=2061, ...
b=2083, ...
b=2100, 1, 2, ...
b=212...
b=214...
b=216不可能,因为216=6^3
b=218...
b=2202, ...
b=2220, ...
b=2241, ...
b=2260, ...
b=2280, 2, ...
b=2301, ...
b=2320, ...
b=2347, ...
b=2361, ...
b=2380, 2, ...
b=2400, 1, 3, ...
b=2422, 3, ...
b=244...
b=246...
b=2482, 4, ...
b=2500, 1, ...
b=252...
b=2542, ...
b=256请参见下方b=2
b=258...
b=2601, ...
b=2620, ...
b=2641, ...
b=2662, ...
b=2680, ...
b=2700, 1, ...
b=2722, ...
b=2746, ...
b=2760, 2, ...
b=2782, 8, ...
b=2800, 1, ...
b=2820, ...
b=2841, ...
b=286...
b=2882, 3, 4, ...
b=2903, ...
b=2920, ...
b=294...
b=2962, ...
b=298...
b=3001, 6, ...
b=302...
b=304...
b=3060, 1, 3, 4, ...
b=308...
b=3100, ...
b=3120, 2, ...
b=3141, ...
b=3160, ...
b=3184, ...
b=3202, ...
b=322...
b=324请参见下方b=18
b=3261, ...
b=3282, ...
b=3300, 4, ...
b=3325, ...
b=3342, ...
b=3360, ...
b=338...
b=3401, 2, ...
b=3425, ...
b=344...
b=3460, ...
b=3480, 4, ...
b=3501, ...
b=3520, 2, ...
b=354...
b=356...
b=3580, ...
b=3605, ...
b=362...
b=3642, ...
b=3660, ...
b=368...
b=3704, ...
b=3720, ...
b=3742, ...
b=3765, ...
b=3780, 3, ...
b=380...
b=3820, 4, ...
b=3841, ...
b=3861, ...
b=3880, ...
b=390...
b=3923, ...
b=394...
b=3960, 1, 4, ...
b=398...
b=400请参见下方b=20
b=402...
b=404...
b=4061, ...
b=4080, ...
b=410...
b=4126, ...
b=4142, ...
b=416...
b=4180, ...
b=4200, 1, ...
b=422...
b=424...
b=4263, ...
b=4285, ...
b=4300, 1, 2, 5, ...
b=4320, 5, ...
b=4343, ...
b=4361, 2, ...
b=4380, ...
b=4401, ...
b=4420, 2, 3, ...
b=4441, ...
b=446...
b=4480, 5, ...
b=450...
b=4524, ...
b=454...
b=4560, 4, ...
b=458...
b=4600, ...
b=4620, ...
b=4641, ...
b=4660, 1, 2, ...
b=468...
b=4701, 4, ...
b=4722, ...
b=4741, 4, ...
b=4762, 4, ...
b=4780, 4, ...
b=480...
b=482...
b=484请参见下方b=22
b=4860, ...
b=4882, ...
b=4900, 1, ...
b=4922, ...
b=4942, ...
b=4961, ...
b=4980, 2, ...
b=500...
b=5020, ...
b=5042, ...
b=5067, ...
b=5080, 3, ...
b=5103, ...
b=512不可能,因为512=8^3
b=514...
b=5162, ...
b=518...
b=5200, ...
b=5220, ...
b=524...
b=5262, ...
b=528...
b=530...
b=5327, ...
b=534...
b=5361, ...
b=538...
b=5400, 2, 3, ...
b=5423, ...
b=5441, ...
b=5460, ...
b=5487, ...
b=5502, ...
b=552...
b=5542, ...
b=5560, 1, 2, ...
b=558...
b=5604, ...
b=5620, 3, 5, 6, ...
b=564...
b=5662, ...
b=5680, 2, 4, ...
b=5700, 1, ...
b=572...
b=574...
b=576请参见下方b=24
b=578...
b=580...
b=5822, ...
b=5841, 2, ...
b=5860, ...
b=5885, ...
b=590...
b=5920, 6, ...
b=5941, ...
b=5963, ...
b=5980, 4, ...
b=6000, 2, ...
b=602...
b=604...
b=6060, ...
b=608...
b=6103, ...
b=6120, ...
b=6148, ...
b=6160, 2, ...
b=6180, ...
b=620...
b=622...
b=6242, ...
b=626...
b=6282, ...
b=6300, ...
b=632...
b=6341, ...
b=6361, ...
b=638...
b=6400, ...
b=6420, 4, ...
b=6441, ...
b=6460, 1, ...
b=648...
b=650...
b=6520, ...
b=6541, ...
b=6562, ...
b=6580, ...
b=6600, ...
b=662...
b=6643, ...
b=666...
b=668...
b=670...
b=6720, ...
b=6741, ...
b=676请参见下方b=26
b=678...
b=6801, 3, ...
b=6820, 3, ...
b=684...
b=6861, 4, ...
b=6884, ...
b=6900, 1, 2, 4, ...
b=692...
b=694...
b=6961, ...
b=698...
b=7000, 1, ...
b=7022, ...
b=7041, ...
b=706...
b=7080, ...
b=7102, ...
b=712...
b=7141, ...
b=7161, ...
b=7180, ...
b=720...
b=722...
b=724...
b=7260, 5, ...
b=7286, ...
b=7302, ...
b=7320, 2, 3, ...
b=734...
b=7364, ...
b=7380, 2, 5, ...
b=7401, ...
b=7420, 2, ...
b=744...
b=746...
b=7482, ...
b=7500, 1, ...
b=752...
b=754...
b=7560, ...
b=7582, ...
b=7600, 1, 2, ...
b=762...
b=7641, ...
b=766...
b=7680, 2, ...
b=770...
b=7720, 2, ...
b=7744, ...
b=7764, ...
b=7782, 4, ...
b=7801, ...
b=7823, ...
b=784请参见下方b=28
b=7860, 2, ...
b=7882, ...
b=7904, ...
b=792...
b=794...
b=7960, ...
b=7982, ...
b=8002, 3, ...
b=802...
b=8045, ...
b=806...
b=8080, 3, ...
b=8100, 2, ...
b=812...
b=814...
b=8161, ...
b=818...
b=8200, ...
b=8220, ...
b=82410, ...
b=8260, 1, ...
b=8280, ...
b=8304, ...
b=8324, ...
b=8344, ...
b=836...
b=8380, ...
b=840...
b=842...
b=844...
b=8464, ...
b=848...
b=8505, ...
b=8520, ...
b=854...
b=8560, 2, ...
b=8580, ...
b=8601, ...
b=8620, ...
b=8641, ...
b=8663, ...
b=868...
b=870...
b=872...
b=8742, ...
b=8760, 3, ...
b=878...
b=8800, ...
b=8820, ...
b=8843, 5, ...
b=8860, ...
b=888...
b=8901, ...
b=8923, 8, ...
b=8942, ...
b=896...
b=8988, ...
b=900请参见下方b=30
b=902...
b=904...
b=9060, 1, ...
b=908...
b=9100, 1, ...
b=9122, ...
b=9142, ...
b=9163, 4, ...
b=9180, 3, ...
b=9201, ...
b=922...
b=924...
b=926...
b=9280, 2, ...
b=9301, 2, ...
b=932...
b=9343, ...
b=9360, 1, 2, ...
b=938...
b=9400, ...
b=942...
b=944...
b=9460, 1, 4, ...
b=948...
b=9501, ...
b=9520, 2, ...
b=954...
b=9563, 4, ...
b=958...
b=9601, 7, ...
b=9622, ...
b=964...
b=9660, 1, 2, ...
b=968...
b=9700, ...
b=9724, ...
b=974...
b=9760, ...
b=978...
b=980...
b=9820, 4, ...
b=9844, ...
b=9861, 2, ...
b=988...
b=9900, 3, ...
b=9922, ...
b=994...
b=9960, 2, ...
b=998...
b=1000不可能,因为1000=10^3

(彩色单元格对应于斯隆的A075090.)

省略号(圆点)表示没有其他已知术语。它不一定暗示序列继续。可以推测,上表中的每一行都是有限序列。

有几种方法可以从上面定义新的整数序列table:连接所有行。或者给出每行中的术语数。或者列出其序列为空的行号。这些序列都不是出现在斯隆的.但由于每行中可能有尚未发现的术语最好不要提交这些序列。

弗斯特b对于其中n个出现在以下行中:A056993号

弗斯特b其中0、1、2、…、。。。,n个出现在以下行中:A090872号

最大已知值n个

下表的灵感来自伊夫加洛特的页面.这里我们给出了最大的已知值n个请注意更新此页面后,可能会发现新的素数。

目前已知的基地b 组织环境信息系统
n个>22 (无)
n个=222^n个=4194304(无)
n个=212^n个=2097152(无)
n个=202^n个=1048576919444, 1059094, 1951734, 1963736.A321323飞机
n个=192^n个=52428875898、341112、356926、475856、1880370、2061748、2312092、2733014、2788032、2877652等。A243959型
n个=182^n个=26214424518、40734、145310、361658、525094、676754、773620、1415198、1488256、1615588等。A244150型
n个=172^n个=13107262722、130816、228188、386892、572186、689186、909548、1063730、1176694、1361244等。A253854型
n个=162^n个=6553648594、108368、141146、189590、255694、291726、292550、357868、440846、544118等A251597型
n个=152^n个=3276870906、167176、204462、249830、321164、330716、332554、429370、499310、524552等226530英镑
n个=142^n个=1638467234101830114024133858162192165306210714216968229310232798等A226529号

在上表中,不能保证显示的底座是最小的可能。

请参见:


/杰佩森