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?

 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

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

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