Having learned from the experience of creating left truncable semiprimes in the previous post, I won't try creating the longest possible chain associated with a given semiprime. Instead, starting with a given semiprime, digits 0 to 9 will be added to the right of the semiprime until a semiprime is found and the process repeated until none of the digits from 0 to 9 can create a semiprime. Let's start with the first semiprime 6 = 2 x 3 (permalink):
Semiprime | Factorisation --------------------------------------------- 6 | 2 * 3 62 | 2 * 31 622 | 2 * 311 6227 | 13 * 479 62277 | 3 * 20759 622771 | 23 * 27077 6227711 | 7 * 889673 62277118 | 2 * 31138559 622771187 | 1889 * 329683 6227711873 | 65267 * 95419 62277118733 | 137 * 454577509 622771187339 | 7 * 88967312477 6227711873391 | 3 * 2075903957797 62277118733913 | 3 * 20759039577971
Next we have 10 = 2 x 5 (permalink):
Semiprime | Factorisation --------------------------------------------- 10 | 2 * 5 106 | 2 * 53 1067 | 11 * 97 10671 | 3 * 3557 106717 | 13 * 8209 1067173 | 19 * 56167 10671731 | 7 * 1524533 106717315 | 5 * 21343463 1067173151 | 11 * 97015741 10671731513 | 653 * 16342621 106717315135 | 5 * 21343463027 1067173151351 | 523 * 2040484037
Next we have 14 = 2 x 7 (permalink).
Semiprime | Factorisation --------------------------------------------- 14 | 2 * 7 141 | 3 * 47 1411 | 17 * 83 14111 | 103 * 137 141119 | 11 * 12829 1411193 | 7 * 201599 14111933 | 11 * 1282903 141119339 | 83 * 1700233
Next we have 15 = 3 x 5 (permalink).
Semiprime | Factorisation --------------------------------------------- 15 | 3 * 5 155 | 5 * 31 1555 | 5 * 311 15553 | 103 * 151 155531 | 43 * 3617
Now we'll try 21 = 3 x 7 (permalink).
Semiprime | Factorisation --------------------------------------------- 21 | 3 * 7 213 | 3 * 71 2138 | 2 * 1069 21381 | 3 * 7127 213811 | 13 * 16447 2138111 | 61 * 35051 21381117 | 3 * 7127039
Let's try a larger number like 28293.
Semiprime | Factorisation --------------------------------------------- 28293 | 3 * 9431 282937 | 31 * 9127 2829371 | 1571 * 1801 28293711 | 3 * 9431237 282937111 | 15959 * 17729 2829371119 | 331 * 8547949
Clearly the chains are shorter when creating right truncatable semiprimes.
No comments:
Post a Comment