# 唯一素数

$\frac{\Phi_n(10)}{\gcd(\Phi_n(10),n)} = p^c$

1 3
2 11
3 37
4 101
10 9,091
12 9,901
9 333,667
14 909,091
24 99,990,001
36 999,999,000,001
48 9,999,999,900,000,001
38 909,090,909,090,909,091
19 1,111,111,111,111,111,111
23 11,111,111,111,111,111,111,111
39 900,900,900,900,990,990,990,991
62 909,090,909,090,909,090,909,090,909,091
120 100,009,999,999,899,989,999,000,000,010,001
150 10,000,099,999,999,989,999,899,999,000,000,000,100,001
106 9,090,909,090,909,090,909,090,909,090,909,090,909,090,909,090,909,091
93 900,900,900,900,900,900,900,900,900,900,990,990,990,990,990,990,990,990,990,991
134 909,090,909,090,909,090,909,090,909,090,909,090,909,090,909,090,909,090,909,090,909,091
294 142,857,157,142,857,142,856,999,999,985,714,285,714,285,857,142,857,142,855,714,285,571,428,571,428,572,857,143
196 999,999,999,999,990,000,000,000,000,099,999,999,999,999,000,000,000,000,009,999,999,999,999,900,000,000,000,001

## 二進制中的唯一質數

3, 5, 7, 11, 13, 17, 19, 31, 41, 43, 73, 127, 151, 241, 257, 331, 337, 683, ...... （OEIS中的数列A144755）：

2 3 11
4 5 101
3 7 111
10 11 1011
12 13 1101
8 17 1 0001
18 19 1 0011
5 31 1 1111
20 41 10 1001
14 43 10 1011
9 73 100 1001
7 127 111 1111
15 151 1001 0111
24 241 1111 0001
16 257 1 0000 0001
30 331 1 0100 1011
21 337 1 0101 0001
22 683 10 1010 1011
26 2,731 1010 1010 1011
42 5,419 1 0101 0010 1011
13 8,191 1 1111 1111 1111
34 43,691 1010 1010 1010 1011
40 61,681 1111 0000 1111 0001
32 65,537 1 0000 0000 0000 0001
54 87,211 1 0101 0100 1010 1011
17 131,071 1 1111 1111 1111 1111
38 174,763 10 1010 1010 1010 1011
27 262,657 100 0000 0010 0000 0001
19 524,287 111 1111 1111 1111 1111
33 599,479 1001 0010 0101 1011 0111
46 2,796,203 10 1010 1010 1010 1010 1011
56 15,790,321 1111 0000 1111 0000 1111 0001
90 18,837,001 1 0001 1111 0110 1110 0000 1001
78 22,366,891 1 0101 0101 0100 1010 1010 1011
62 715,827,883 10 1010 1010 1010 1010 1010 1010 1011
31 2,147,483,647 111 1111 1111 1111 1111 1111 1111 1111
80 4,278,255,361 1111 1111 0000 0000 1111 1111 0000 0001
120 4,562,284,561 1 0000 1111 1110 1110 1111 0000 0001 0001
126 77,158,673,929 1 0001 1111 0111 0000 0011 1110 1110 0000 1001
150 1,133,836,730,401 1 0000 0111 1111 1101 1110 1111 1000 0000 0010 0001
86 2,932,031,007,403 10 1010 1010 1010 1010 1010 1010 1010 1010 1010 1011
98 4,363,953,127,297 11 1111 1000 0000 1111 1110 0000 0011 1111 1000 0001
49 4,432,676,798,593 100 0000 1000 0001 0000 0010 0000 0100 0000 1000 0001
69 10,052,678,938,039 1001 0010 0100 1001 0010 0101 1011 0110 1101 1011 0111
65 145,295,143,558,111 1000 0100 0010 0101 0010 1001 0110 1011 0101 1011 1101 1111
174 96,076,791,871,613,611 1 0101 0101 0101 0101 0101 0101 0100 1010 1010 1010 1010 1010 1010 1011
77 581,283,643,249,112,959 1000 0001 0001 0010 0010 0110 0100 1100 1101 1001 1011 1011 0111 0111 1111
93 658,812,288,653,553,079 1001 0010 0100 1001 0010 0100 1001 0011 0110 1101 1011 0110 1101 1011 0111
122 768,614,336,404,564,651 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1011
61 2,305,843,009,213,693,951 1 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111
85 9,520,972,806,333,758,431 1000 0100 0010 0001 0100 1010 0101 0010 1011 0101 1010 1101 0111 1011 1101 1111
192 18,446,744,069,414,584,321 1111 1111 1111 1111 1111 1111 1111 1111 0000 0000 0000 0000 0000 0000 0000 0001