A **"father" prime** shall be defined as one for which **the sum of the squares of its digits** is also a **prime**. The sum is therefore the **"child" prime**.

An example of an ancestral line of fathers and children might be this:

191 is father to 83 and grandfather to 73; 83 is father to 73; but 73 is "childless", as the sum (58) of the squares of its two digits (7 and 3) is a composite number. Hence, it is "the end of the line".

The longest ancestral lines so far established have 5 generations. One example of these is

Problem: Find a "father" and "grandfather" for 1499.

All two-digit fathers are given here.

11: 1

23: 2

41: 4

61: 6

83: 8

% % %

list of father-child primes: 100 < Prime fathers < 1000.

prime child | no. of fathers | |

113, 131, 311 | ||

223, 401 | ||

313, 331 | ||

601 | ||

443 | ||

353 | ||

461, 641 | ||

137, 173, 317 | ||

463, 643 | ||

337, 373. 733 | ||

661 | ||

191, 911 | ||

229 | ||

409 | ||

467, 647 | ||

773 | ||

683, 863 | ||

449 | ||

179, 197, 719, 971 | ||

883 | ||

379, 397, 739, 937 | ||

829 | ||

199, 919, 991 | ||

797, 977 | ||

997 | ||

47 | . |

113: 1

131: same result.

311: emirp for 113; is the 11th term in the list of odd prime sums

173: same 317: same

371: 7 x 53 [

713: 23 x 31

731: 17 x 43

337: 3

373: same

733: same

179: 1

197: same

719: same

791: 7 x 113

917: 7 x 131

971: same

[note: 449 -(ssd)-> 113, a permutation of 131.]

379: 3

397: same

739: same

793: 13 x 61

937: same

973: 7 x 139 [7's co-factor is the "ssd" sum of this group]

199: 1

919: same

991: same; emirp for 199.

Decade trios:

461 yields 53 641 yields 53

463 yields 61 643 yields 61

467 yields 101 647 yields 101

Strings:

179 gvs 131 gvs 11 gvs 2

191 gvs 83 gvs 73

463 gvs 61 gvs 37

443 gvs 41 gvs 17

111611 [or 611111] gvs 41 gvs 17

22441 [or 24421, or 44221] gvs 41 gvs 17

449 to 131 to 11 to 2

449 div by 81 = 5 r 44

so five 9's, and 6, 2, & 2 could be used.

22699999/no

26299999/no

62299999/yes, a prime

1699 gvs 199 gvs 163

1499 gvs 179 gvs 131 gvs 11 gvs 2; which is the one given at the top.

1499 -- > 1 + 16 + 81 + 81 = 179

179 --- > 1 + 49 + 81 = 131

131 --- > 1 + 9 + 1 = 11

11 --- > 1 + 1 = 2

1499 prime | 4199 no | 9149 no | 9419 prime |

1949 prime | 4919 prime | 9194 no | 9491 prime |

1994 no | 4991 no | 9914 no | 9941 prime |

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