Cullen number
Generalizations
Sometimes, a generalized Cullen number base b is defined to be a number of the form n × bⁿ + 1, where n + 2 > b; if a prime can be written in this form, it is then called a generalized Cullen prime.

Cullen number

Section Title: Generalizations
Table Section Text: Sometimes, a generalized Cullen number base b is defined to be a number of the form n × bⁿ + 1, where n + 2 > b; if a prime can be written in this form, it is then called a generalized Cullen prime.

b	numbers n such that n × bn + 1 is prime (these n are checked up to 101757)	OEIS sequence

1	1, 2, 4, 6, 10, 12, 16, 18, 22, 28, 30, 36, 40, 42, 46, 52, 58, 60, 66, 70, 72, 78, 82, 88, 96, 100, 102, 106, 108, 112, 126, 130, 136, 138, 148, 150, 156, 162, 166, 172, 178, 180, 190, 192, 196, 198, 210, 222, 226, 228, 232, 238, 240, 250, 256, 262, 268, 270, 276, 280, 282, 292, ...	A006093

2	1, 141, 4713, 5795, 6611, 18496, 32292, 32469, 59656, 90825, 262419, 361275, 481899, 1354828, 6328548, 6679881, ...	A005849

3	2, 8, 32, 54, 114, 414, 1400, 1850, 2848, 4874, 7268, 19290, 337590, 1183414, ...	A006552

4	1, 3, 7, 33, 67, 223, 663, 912, 1383, 3777, 3972, 10669, 48375, ...	A007646

5	1242, 18390, ...

6	1, 2, 91, 185, 387, 488, 747, 800, 9901, 10115, 12043, 13118, 30981, 51496, ...	A242176

7	34, 1980, 9898, ...	A242177

8	5, 17, 23, 1911, 20855, 35945, 42816, ..., 749130, ...	A242178

9	2, 12382, 27608, 31330, 117852, ...	A265013

10	1, 3, 9, 21, 363, 2161, 4839, 49521, 105994, 207777, ...	A007647

11	10, ...

12	1, 8, 247, 3610, 4775, 19789, 187895, ...	A242196

13	...

14	3, 5, 6, 9, 33, 45, 243, 252, 1798, 2429, 5686, 12509, 42545, ...	A242197

15	8, 14, 44, 154, 274, 694, 17426, 59430, ...	A242198

16	1, 3, 55, 81, 223, 1227, 3012, 3301, ...	A242199

17	19650, 236418, ...

18	1, 3, 21, 23, 842, 1683, 3401, 16839, 49963, 60239, 150940, 155928, ...	A007648

19	6460, ...

20	3, 6207, 8076, 22356, 151456, ...

21	2, 8, 26, 67100, ...

22	1, 15, 189, 814, 19909, 72207, ...

23	4330, 89350, ...

24	2, 8, 368, ...

25	...

26	117, 3143, 3886, 7763, 64020, 88900, ...

27	2, 56, 23454, ..., 259738, ...

28	1, 48, 468, 2655, 3741, 49930, ...

29	...

30	1, 2, 3, 7, 14, 17, 39, 79, 87, 99, 128, 169, 221, 252, 307, 3646, 6115, 19617, 49718, ...

Sentence(s)

The Cullen primes are those for n: 1, 141, 4713, 5795, 6611, 18496, 32292, 32469, 59656, 90825, 262419, 361275, 481899, 1354828, 6328548, 6679881 (sequence A005849 in the OEIS).

final_sentence: The Cullen primes are those for n: 1, 141, 4713, 5795, 6611, 18496, 32292, 32469, 59656, 90825, 262419, 361275, 481899, 1354828, 6328548, 6679881 (sequence A005849 in the OEIS).