A prime whose digital reverse is a different prime. more
The first 600 emirps :
13,
17,
31,
37,
71,
73,
79,
97,
107,
113,
149,
157,
167,
179,
199,
311,
337,
347,
359,
389,
701,
709,
733,
739,
743,
751,
761,
769,
907,
937,
941,
953,
967,
971,
983,
991,
1009,
1021,
1031,
1033,
1061,
1069,
1091,
1097,
1103,
1109,
1151,
1153,
1181,
1193,
1201,
1213,
1217,
1223,
1229,
1231,
1237,
1249,
1259,
1279,
1283,
1301,
1321,
1381,
1399,
1409,
1429,
1439,
1453,
1471,
1487,
1499,
1511,
1523,
1559,
1583,
1597,
1601,
1619,
1657,
1669,
1723,
1733,
1741,
1753,
1789,
1811,
1831,
1847,
1867,
1879,
1901,
1913,
1933,
1949,
1979,
3011,
3019,
3023,
3049,
3067,
3083,
3089,
3109,
3121,
3163,
3169,
3191,
3203,
3221,
3251,
3257,
3271,
3299,
3301,
3319,
3343,
3347,
3359,
3371,
3373,
3389,
3391,
3407,
3433,
3463,
3467,
3469,
3511,
3527,
3541,
3571,
3583,
3613,
3643,
3697,
3719,
3733,
3767,
3803,
3821,
3851,
3853,
3889,
3911,
3917,
3929,
7027,
7043,
7057,
7121,
7177,
7187,
7193,
7207,
7219,
7229,
7253,
7297,
7321,
7349,
7433,
7457,
7459,
7481,
7507,
7523,
7529,
7547,
7561,
7577,
7589,
7603,
7643,
7649,
7673,
7681,
7687,
7699,
7717,
7757,
7817,
7841,
7867,
7879,
7901,
7927,
7949,
7951,
7963,
9001,
9011,
9013,
9029,
9041,
9103,
9127,
9133,
9161,
9173,
9209,
9221,
9227,
9241,
9257,
9293,
9341,
9349,
9403,
9421,
9437,
9439,
9467,
9479,
9491,
9497,
9521,
9533,
9547,
9551,
9601,
9613,
9643,
9661,
9679,
9721,
9749,
9769,
9781,
9787,
9791,
9803,
9833,
9857,
9871,
9883,
9923,
9931,
9941,
9967,
10007,
10009,
10039,
10061,
10067,
10069,
10079,
10091,
10151,
10159,
10177,
10247,
10253,
10273,
10321,
10333,
10343,
10391,
10429,
10453,
10457,
10459,
10487,
10499,
10613,
10639,
10651,
10711,
10739,
10781,
10853,
10859,
10867,
10889,
10891,
10909,
10939,
10987,
10993,
11003,
11057,
11071,
11083,
11149,
11159,
11161,
11197,
11243,
11257,
11329,
11353,
11423,
11447,
11489,
11497,
11551,
11579,
11587,
11593,
11621,
11657,
11677,
11699,
11701,
11717,
11719,
11731,
11777,
11779,
11783,
11789,
11833,
11839,
11897,
11903,
11909,
11923,
11927,
11933,
11939,
11953,
11959,
11969,
11971,
11981,
12071,
12073,
12107,
12109,
12113,
12119,
12149,
12227,
12241,
12253,
12269,
12289,
12301,
12323,
12373,
12437,
12491,
12547,
12553,
12577,
12611,
12619,
12641,
12659,
12689,
12697,
12713,
12743,
12757,
12763,
12799,
12809,
12829,
12841,
12893,
12907,
12919,
12983,
13009,
13043,
13147,
13151,
13159,
13163,
13259,
13267,
13291,
13297,
13337,
13441,
13457,
13469,
13477,
13499,
13513,
13523,
13553,
13591,
13597,
13619,
13693,
13697,
13709,
13711,
13751,
13757,
13759,
13781,
13789,
13829,
13841,
13873,
13903,
13933,
13963,
14029,
14057,
14071,
14081,
14087,
14107,
14143,
14153,
14177,
14207,
14221,
14251,
14293,
14303,
14323,
14327,
14387,
14423,
14431,
14447,
14449,
14479,
14519,
14549,
14551,
14557,
14563,
14591,
14593,
14621,
14629,
14633,
14657,
14713,
14717,
14821,
14831,
14843,
14879,
14891,
14897,
14923,
14929,
14939,
14947,
14957,
15013,
15053,
15091,
15101,
15131,
15139,
15149,
15227,
15241,
15263,
15289,
15299,
15307,
15349,
15377,
15383,
15461,
15493,
15497,
15511,
15527,
15541,
15601,
15643,
15649,
15661,
15667,
15679,
15683,
15731,
15733,
15737,
15791,
15803,
15907,
15919,
15937,
15973,
16001,
16007,
16063,
16073,
16103,
16111,
16127,
16193,
16217,
16223,
16249,
16267,
16427,
16433,
16451,
16453,
16481,
16493,
16547,
16567,
16573,
16603,
16651,
16691,
16699,
16729,
16747,
16763,
16829,
16879,
16883,
16937,
16943,
16979,
17011,
17021,
17033,
17041,
17047,
17117,
17203,
17207,
17209,
17383,
17393,
17417,
17443,
17467,
17477,
17491,
17519,
17573,
17579,
17599,
17627,
17669,
17681,
17683,
17713,
17737,
17747,
17749,
17827,
17839,
17863,
17903,
17909,
17911,
17923,
17939,
17959,
18013,
18041,
18077,
18089,
18133,
18169,
18191,
18199,
18253,
18269,
18307,
18329,
18353,
18379,
18413,
18427,
18439,
18461,
18539,
18593,
18637,
18671,
18691,
18701,
18719,
18731,
18743,
18749,
18757,
18773,
18787,
18803,
18859,
18899,
18911,
18913,
19001,
19013,
19037,
19051,
19163,
19181,
19219,
19231,
19237.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 1722796 values, from 13 to 199999931).
n\r | 0 | 1 |
2 | 0 | 1722796 | 2 |
3 | 0 | 861759 | 861037 | 3 |
4 | 0 | 861065 | 0 | 861731 | 4 |
5 | 0 | 453792 | 419684 | 434303 | 415017 | 5 |
6 | 0 | 861759 | 0 | 0 | 0 | 861037 | 6 |
7 | 0 | 286182 | 288157 | 283810 | 287155 | 287661 | 289831 | 7 |
8 | 0 | 430643 | 0 | 430850 | 0 | 430422 | 0 | 430881 | 8 |
9 | 0 | 289082 | 286967 | 0 | 286585 | 286907 | 0 | 286092 | 287163 | 9 |
10 | 0 | 453792 | 0 | 434303 | 0 | 0 | 0 | 419684 | 0 | 415017 | 10 |
11 | 0 | 172389 | 172711 | 171896 | 173484 | 171606 | 171397 | 173039 | 171077 | 172056 | 173141 |
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.