Monday, 21 September 2026

Left and Right Truncatable Triprimes

What was done with left and right truncatable semiprimes can also be done with triprimes. The very first triprime is 8 = 2 x 2 x 2 and, by adding suitable digits to the LEFT, we get (permalink):

Triprime             | Factorisation
---------------------------------------------
8                    | 2 * 2 * 2
18                   | 2 * 3 * 3
318                  | 2 * 3 * 53
2318                 | 2 * 19 * 61
12318                | 2 * 3 * 2053
112318               | 2 * 89 * 631
6112318              | 2 * 101 * 30259
16112318             | 2 * 53 * 152003
216112318            | 2 * 7687 * 14057
4216112318           | 2 * 11 * 191641469
24216112318          | 2 * 73 * 165863783
124216112318         | 2 * 19 * 3268845061
5124216112318        | 2 * 3203 * 799908853
25124216112318       | 2 * 3 * 4187369352053
225124216112318      | 2 * 431 * 261164983889
2225124216112318     | 2 * 193 * 5764570508063

Next we have 12 = 2 x 2 x 3 which gives (permalink):

Triprime             | Factorisation
---------------------------------------------
12                   | 2 * 2 * 3
212                  | 2 * 2 * 53
5212                 | 2 * 2 * 1303
15212                | 2 * 2 * 3803
315212               | 2 * 2 * 78803
2315212              | 2 * 2 * 578803

The next triprime (18) gives the same chain as did 8. 

Let's try adding digits to the RIGHT this time. Starting with 8 we don't get very far as no digit when adding to the right of 8 will produce a triprime. However, with 12 we have more success (permalink):

Triprime             | Factorisation
---------------------------------------------
12                   | 2 * 2 * 3
124                  | 2 * 2 * 31
1244                 | 2 * 2 * 311
12445                | 5 * 19 * 131
124453               | 7 * 23 * 773
1244534              | 2 * 349 * 1783
12445341             | 3 * 167 * 24841
124453414            | 2 * 23 * 2705509
1244534143           | 19 * 19 * 3447463
12445341431          | 769 * 2053 * 7883
124453414317         | 3 * 23789 * 1743851
1244534143173        | 3 * 31 * 13382087561
12445341431731       | 13 * 887 * 1079294201

The next triprime (18) produces this chain (permalink):

Triprime             | Factorisation
---------------------------------------------
18                   | 2 * 3 * 3
182                  | 2 * 7 * 13
1825                 | 5 * 5 * 73
18255                | 3 * 5 * 1217
182553               | 3 * 7 * 8693
1825534              | 2 * 227 * 4021
18255345             | 3 * 5 * 1217023
182553451            | 31 * 331 * 17791
1825534511           | 17 * 967 * 111049
18255345115          | 5 * 7 * 521581289
182553451151         | 17 * 5147 * 2086349
1825534511511        | 3 * 53 * 11481349129

With a large triprime like 28282 = 2 x 79 x 179 we end up with (permalink):

Triprime             | Factorisation
---------------------------------------------
28282                | 2 * 79 * 179
282821               | 7 * 11 * 3673
2828211              | 3 * 619 * 1523
28282113             | 3 * 3 * 3142457
282821134            | 2 * 5099 * 27733
2828211341           | 17 * 29 * 5736737
28282113411          | 3 * 32621 * 288997
282821134111         | 43 * 563 * 11682479
2828211341111        | 13 * 26591 * 8181517
28282113411116       | 2 * 2 * 7070528352779
282821134111163      | 59 * 1307821 * 3665317
So the program is working well.

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