## The twin primes (4241, 4243)

4241   and   4243   form a twin prime pair.

They are of the form   $(10^n) \, a \; + a \; \pm \; 1$

where   $a$   consists of   $n$   digits.

>>   Are there more such twin primes of 4 digits each?

>>   Do there exist other twin primes of that type consisting of 6 and 8 digits?

math grad - Interest: Number theory
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### 2 Responses to The twin primes (4241, 4243)

1. pipo says:

There is one more twin prime pair of 4 digits.
And eighteen combinations of 6 digits, and forty-four combinations of 8 digits, among them also 42424242 ± 1

42 4243 4241
78 7879 7877
102 102103 102101
108 108109 108107
180 180181 180179
192 192193 192191
270 270271 270269
300 300301 300299
312 312313 312311
330 330331 330329
342 342343 342341
390 390391 390389
420 420421 420419
522 522523 522521
540 540541 540539
612 612613 612611
660 660661 660659
822 822823 822821
840 840841 840839
882 882883 882881
1002 10021003 10021001
1140 11401141 11401139
1230 12301231 12301229
1272 12721273 12721271
1482 14821483 14821481
1542 15421543 15421541
1632 16321633 16321631
1770 17701771 17701769
2100 21002101 21002099
2190 21902191 21902189
2682 26822683 26822681
2742 27422743 27422741
3072 30723073 30723071
3198 31983199 31983197
3408 34083409 34083407
3642 36423643 36423641
3828 38283829 38283827
4242 42424243 42424241
4452 44524453 44524451
4572 45724573 45724571
4740 47404741 47404739
4788 47884789 47884787
4998 49984999 49984997
5622 56225623 56225621
5718 57185719 57185717
5832 58325833 58325831
6102 61026103 61026101
6258 62586259 62586257
7428 74287429 74287427
7740 77407741 77407739
7938 79387939 79387937
8370 83708371 83708369
8472 84728473 84728471
8610 86108611 86108609
8790 87908791 87908789
8820 88208821 88208819
8832 88328833 88328831
8988 89888989 89888987
9072 90729073 90729071
9120 91209121 91209119
9192 91929193 91929191
9210 92109211 92109209
9330 93309331 93309329
9702 97029703 97029701

pipo