A prime p such that p + 2 is either prime or semiprime. more
The first 600 Chen primes :
2,
3,
5,
7,
11,
13,
17,
19,
23,
29,
31,
37,
41,
47,
53,
59,
67,
71,
83,
89,
101,
107,
109,
113,
127,
131,
137,
139,
149,
157,
167,
179,
181,
191,
197,
199,
211,
227,
233,
239,
251,
257,
263,
269,
281,
293,
307,
311,
317,
337,
347,
353,
359,
379,
389,
401,
409,
419,
431,
443,
449,
461,
467,
479,
487,
491,
499,
503,
509,
521,
541,
557,
563,
569,
571,
577,
587,
599,
617,
631,
641,
647,
653,
659,
677,
683,
701,
719,
743,
751,
761,
769,
787,
797,
809,
811,
821,
827,
829,
839,
857,
863,
877,
881,
887,
911,
919,
937,
941,
947,
953,
971,
977,
983,
991,
1009,
1019,
1031,
1039,
1049,
1061,
1091,
1097,
1109,
1117,
1151,
1163,
1187,
1193,
1201,
1217,
1229,
1259,
1277,
1283,
1289,
1291,
1297,
1301,
1319,
1327,
1361,
1367,
1381,
1399,
1409,
1427,
1439,
1451,
1459,
1471,
1481,
1487,
1499,
1511,
1553,
1559,
1567,
1583,
1601,
1607,
1619,
1621,
1637,
1667,
1669,
1697,
1709,
1721,
1733,
1759,
1777,
1787,
1801,
1847,
1871,
1877,
1889,
1901,
1907,
1913,
1931,
1949,
1979,
1997,
2003,
2017,
2027,
2029,
2039,
2069,
2081,
2087,
2099,
2111,
2129,
2141,
2153,
2179,
2207,
2213,
2237,
2243,
2251,
2267,
2269,
2281,
2309,
2333,
2339,
2351,
2357,
2381,
2389,
2393,
2411,
2417,
2441,
2447,
2459,
2467,
2477,
2531,
2543,
2549,
2557,
2579,
2591,
2609,
2621,
2647,
2657,
2659,
2687,
2699,
2711,
2719,
2729,
2731,
2741,
2777,
2789,
2801,
2837,
2843,
2857,
2861,
2879,
2897,
2909,
2927,
2939,
2957,
2963,
2969,
2971,
2999,
3011,
3037,
3041,
3061,
3083,
3089,
3119,
3137,
3167,
3181,
3187,
3191,
3203,
3221,
3251,
3257,
3259,
3271,
3299,
3307,
3329,
3347,
3359,
3371,
3389,
3407,
3413,
3457,
3461,
3467,
3491,
3511,
3527,
3539,
3541,
3557,
3559,
3581,
3593,
3637,
3659,
3671,
3677,
3691,
3709,
3719,
3761,
3767,
3779,
3797,
3803,
3821,
3847,
3851,
3863,
3881,
3889,
3907,
3917,
3919,
3929,
3947,
3989,
4001,
4007,
4019,
4049,
4091,
4099,
4127,
4133,
4139,
4157,
4211,
4217,
4229,
4241,
4259,
4271,
4283,
4289,
4297,
4337,
4339,
4349,
4357,
4391,
4397,
4409,
4421,
4441,
4447,
4451,
4481,
4517,
4547,
4567,
4591,
4637,
4643,
4649,
4657,
4679,
4703,
4721,
4733,
4787,
4789,
4799,
4801,
4817,
4861,
4871,
4889,
4909,
4931,
4937,
4967,
4969,
4987,
4999,
5009,
5021,
5039,
5051,
5077,
5087,
5099,
5147,
5153,
5167,
5171,
5189,
5197,
5231,
5261,
5279,
5297,
5303,
5309,
5347,
5351,
5381,
5387,
5399,
5417,
5431,
5441,
5471,
5477,
5483,
5501,
5507,
5519,
5531,
5581,
5639,
5651,
5657,
5669,
5701,
5711,
5737,
5741,
5791,
5801,
5807,
5813,
5849,
5851,
5867,
5879,
5897,
5903,
5939,
5981,
5987,
6007,
6011,
6029,
6047,
6079,
6089,
6101,
6113,
6131,
6143,
6197,
6247,
6257,
6269,
6287,
6299,
6311,
6317,
6329,
6337,
6359,
6421,
6427,
6449,
6481,
6491,
6521,
6551,
6569,
6581,
6607,
6619,
6637,
6659,
6661,
6689,
6701,
6709,
6737,
6761,
6779,
6791,
6803,
6827,
6833,
6841,
6863,
6869,
6899,
6911,
6947,
6959,
6971,
6977,
6997,
7001,
7039,
7043,
7069,
7079,
7109,
7121,
7127,
7129,
7151,
7177,
7193,
7211,
7229,
7247,
7253,
7307,
7309,
7321,
7331,
7349,
7417,
7433,
7451,
7457,
7481,
7487,
7499,
7507,
7517,
7529,
7541,
7547,
7559,
7561,
7589,
7591,
7607,
7649,
7669,
7727,
7757,
7793,
7817,
7829,
7853,
7877,
7901,
7907,
7919,
7937,
7949,
8009,
8011,
8059,
8069,
8081,
8087,
8093,
8117,
8147,
8171,
8191,
8219,
8221,
8231,
8291,
8297,
8329,
8369,
8387,
8389,
8429,
8501,
8527,
8537,
8543,
8581,
8597,
8609,
8627,
8663,
8681,
8689,
8707,
8741,
8747,
8779,
8807,
8819,
8837,
8849,
8861,
8887,
8933,
8951,
8969,
8999,
9001,
9011,
9029,
9041,
9067,
9109,
9181,
9199,
9209,
9221,
9227,
9239,
9257.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 1762579 values, from 2 to 99999971).
n\r | 0 | 1 |
2 | 1 | 1762578 | 2 |
3 | 1 | 313314 | 1449264 | 3 |
4 | 0 | 881171 | 1 | 881407 | 4 |
5 | 1 | 544161 | 544328 | 129818 | 544271 | 5 |
6 | 0 | 313314 | 1 | 1 | 0 | 1449263 | 6 |
7 | 1 | 335287 | 335776 | 335039 | 335684 | 85227 | 335565 | 7 |
8 | 0 | 440611 | 1 | 440898 | 0 | 440560 | 0 | 440509 | 8 |
9 | 0 | 156487 | 483283 | 1 | 156826 | 483316 | 0 | 1 | 482665 | 9 |
10 | 0 | 544161 | 1 | 129818 | 0 | 1 | 0 | 544327 | 0 | 544271 | 10 |
11 | 1 | 189984 | 189756 | 189950 | 190035 | 190038 | 190093 | 190667 | 190502 | 51531 | 190022 |
A pictorial representation of the table above
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.