lpetrich
Contributor
Where I found out about it:
Primes on the Moon (Lunar Arithmetic) - Numberphile - YouTube
Lunar arithmetic was named because it seems "out of this world". It was earlier named "dismal arithmetic", as a pun on "decimal", but that name seemed too depressing.
Addition is done digit-by-digit, and is done with the maximum of the digit values. Multiplication is done much like in ordinary arithmetic, but with digit-by-digit multiplication being the minimum of those digits and overall addition being lunar.
As an example, I will consider 37+74 and 37*74.
In ordinary arithmetic,
37 + 74 = 30 + 7 + 70 + 4 = 100 + 11 = 111
37 * 74 = 30*70 + 30*4 + 7*70 + 7*4 = 2100 + 120 + 490 + 28 = 2000 + (1+1+4)*100 + (2+9+2)*10 + 8 = 2000 + 600 + 30 + 8 = 2738
In lunar arithmetic,
37 + 74 = 30 + 7 + 70 + 4 = max(3,7)*10 + max(7,4) = 77
37 * 74 = 30*70 + 30*4 + 7*70 + 7*4 = min(3,7)*100 + min(3,4)*10 + min(7,7)*10 + min(7,4) = 300 + 30 + 70 + 4 = 374
One can also define "lunar primes", primes whose only lunar-multiplication factors are themselves and 9.
A087097 - OEIS
19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 109, 209, 219, 309, 319, 329, 409, 419, 429, 439, 509, 519, 529, 539, 549, 609, 619, 629, 639, 649, 659, 709, 719, 729, 739, 749, 759, 769, 809, 819, 829, 839, 849, 859, 869, 879, 901, 902, 903, 904, 905, 906, 907, 908, 909, 912, 913, 914, 915, 916, 917, 918, 919, 923, 924, 925, 926, 927, 928, 929, 934, 935, 936, 937, 938, 939, 945, 946, 947, 948, 949, 956, 957, 958, 959, 967, 968, 969, 978, 979, 989, ...
Primes on the Moon (Lunar Arithmetic) - Numberphile - YouTube
Lunar arithmetic was named because it seems "out of this world". It was earlier named "dismal arithmetic", as a pun on "decimal", but that name seemed too depressing.
Addition is done digit-by-digit, and is done with the maximum of the digit values. Multiplication is done much like in ordinary arithmetic, but with digit-by-digit multiplication being the minimum of those digits and overall addition being lunar.
As an example, I will consider 37+74 and 37*74.
In ordinary arithmetic,
37 + 74 = 30 + 7 + 70 + 4 = 100 + 11 = 111
37 * 74 = 30*70 + 30*4 + 7*70 + 7*4 = 2100 + 120 + 490 + 28 = 2000 + (1+1+4)*100 + (2+9+2)*10 + 8 = 2000 + 600 + 30 + 8 = 2738
In lunar arithmetic,
37 + 74 = 30 + 7 + 70 + 4 = max(3,7)*10 + max(7,4) = 77
37 * 74 = 30*70 + 30*4 + 7*70 + 7*4 = min(3,7)*100 + min(3,4)*10 + min(7,7)*10 + min(7,4) = 300 + 30 + 70 + 4 = 374
One can also define "lunar primes", primes whose only lunar-multiplication factors are themselves and 9.
A087097 - OEIS
19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 109, 209, 219, 309, 319, 329, 409, 419, 429, 439, 509, 519, 529, 539, 549, 609, 619, 629, 639, 649, 659, 709, 719, 729, 739, 749, 759, 769, 809, 819, 829, 839, 849, 859, 869, 879, 901, 902, 903, 904, 905, 906, 907, 908, 909, 912, 913, 914, 915, 916, 917, 918, 919, 923, 924, 925, 926, 927, 928, 929, 934, 935, 936, 937, 938, 939, 945, 946, 947, 948, 949, 956, 957, 958, 959, 967, 968, 969, 978, 979, 989, ...