Merge pull request #6332 from drbaggy/master

Primorial -> Achilles

2 files changed, 41 insertions, 0 deletions

diff --git a/challenge-169/james-smith/README.md b/challenge-169/james-smith/README.md
index fb95af0dfc..761ed04166 100644
--- a/challenge-169/james-smith/README.md
+++ b/challenge-169/james-smith/README.md
@@ -237,6 +237,31 @@ Some examples for larger values of `n` are:
 |      325,000 |       81,981,196,443 | 3<sup>3</sup>.55103<sup>2</sup>                              |
 |      350,000 |       94,917,245,000 | 2<sup>3</sup>.5<sup>4</sup>.4357<sup>2</sup>                 |
 |      375,000 |      108,802,180,800 | 2<sup>6</sup>.3<sup>5</sup>.5<sup>2</sup>.23<sup>4</sup>     |
+|      400,000 |      123,623,945,500 | 2<sup>2</sup>.5<sup>3</sup>.11<sup>3</sup>.431<sup>2</sup>   |
+|      425,000 |      139,380,371,325 | 3<sup>6</sup>.5<sup>2</sup>.13<sup>3</sup>.59<sup>2</sup>    |
+|      450,000 |      156,087,946,125 | 3<sup>2</sup>.5<sup>3</sup>.11779<sup>2</sup>                |
+|      475,000 |      173,733,903,648 | 2<sup>5</sup>.3<sup>6</sup>.2729<sup>2</sup>                 |
+|      500,000 |      192,302,155,612 | 2<sup>2</sup>.7<sup>3</sup>.11839<sup>2</sup>                |
+|      525,000 |      211,812,977,475 | 3<sup>2</sup>.5<sup>2</sup>.11<sup>3</sup>.29<sup>4</sup>    |
+|      550,000 |      232,275,648,200 | 2<sup>3</sup>.5<sup>2</sup>.53<sup>2</sup>.643<sup>2</sup>   |
+|      575,000 |      253,653,177,148 | 2<sup>2</sup>.7<sup>3</sup>.13597<sup>2</sup>                |
+|      600,000 |      275,972,670,000 | 2<sup>4</sup>.3<sup>5</sup>.5<sup>4</sup>.337<sup>2</sup>    |
+|      625,000 |      299,230,934,400 | 2<sup>7</sup>.3<sup>3</sup>.5<sup>2</sup>.1861<sup>2</sup>   |
+|      650,000 |      323,432,005,175 | 5<sup>2</sup>.47<sup>3</sup>.353<sup>2</sup>                 |
+|      675,000 |      348,549,042,888 | 2<sup>3</sup>.3<sup>2</sup>.41<sup>2</sup>.1697<sup>2</sup>  |
+|      700,000 |      374,611,070,700 | 2<sup>2</sup>.3<sup>3</sup>.5<sup>2</sup>.11779<sup>2</sup>  |
+|      725,000 |      401,600,467,125 | 3<sup>3</sup>.5<sup>3</sup>.11<sup>3</sup>.13<sup>2</sup>.23<sup>2</sup> |
+|      750,000 |      429,542,144,712 | 2<sup>3</sup>.3<sup>2</sup>.77239<sup>2</sup>                |
+|      775,000 |      458,391,256,875 | 3<sup>2</sup>.5<sup>4</sup>.19<sup>3</sup>.109<sup>2</sup>   |
+|      800,000 |      488,186,710,964 | 2<sup>2</sup>.29<sup>3</sup>.2237<sup>2</sup>                |
+|      825,000 |      518,923,743,752 | 2<sup>3</sup>.257<sup>2</sup>.991<sup>2</sup>                |
+|      850,000 |      550,582,402,248 | 2<sup>3</sup>.3<sup>4</sup>.103<sup>2</sup>.283<sup>2</sup>  |
+|      875,000 |      583,157,667,200 | 2<sup>7</sup>.5<sup>2</sup>.19<sup>3</sup>.163<sup>2</sup>   |
+|      900,000 |      616,689,640,125 | 3<sup>2</sup>.5<sup>3</sup>.13<sup>2</sup>.1801<sup>2</sup>  |
+|      925,000 |      651,153,828,125 | 5<sup>7</sup>.2887<sup>2</sup>                               |
+|      950,000 |      686,540,147,825 | 5<sup>2</sup>.7<sup>3</sup>.431<sup>3</sup>                  |
+|      975,000 |      722,830,618,800 | 2<sup>4</sup>.3<sup>11</sup>.5<sup>2</sup>.101<sup>2</sup>   |
+|    1,000,000 |      760,089,707,712 | 2<sup>6</sup>.3<sup>5</sup>.6991<sup>2</sup>                 |
 
 And these are the first numbers with `n` digits...
 
@@ -253,6 +278,7 @@ And these are the first numbers with `n` digits...
 |     10 |       34,562 |        1,000,042,200 | 2<sup>3</sup>.3<sup>6</sup>.5<sup>2</sup>.19<sup>3</sup>     |
 |     11 |      111,892 |       10,000,373,888 | 2<sup>7</sup>.8839<sup>2</sup>                               |
 |     12 |      359,341 |      100,001,075,328 | 2<sup>7</sup>.3<sup>2</sup>.7<sup>2</sup>.11<sup>6</sup>     |
+|     13 |    1,148,196 |    1,000,002,788,575 | 5<sup>2</sup>.7<sup>3</sup>.10799<sup>2</sup>                |
 
 ### Github formatting script....
 
diff --git a/challenge-170/james-smith/README.md b/challenge-170/james-smith/README.md
index 629ef1711c..b88b247b6e 100644
--- a/challenge-170/james-smith/README.md
+++ b/challenge-170/james-smith/README.md
@@ -45,6 +45,21 @@ say$a=1;forprimes{say$a*=$_}nth_prime 9                # 39 bytes
 say$a=1;forprimes{say$a*=$_}23                         # 30 bytes
 ```
 
+### Aside - Last week's challenge - Achilles numbers.
+
+There is a connection with last weeks challenge here. The lowest Achilles number with `n` distinct prime factors is `2 * P(n)^2`
+
+So we have:
+
+| n  | P(n)     | 2 * P(n)^2      | achilles idx | Factorisation |
+| -: | -------: | --------------: | -----------: | ------------- |
+|  2 |       6  |              72 |            1 | 2<sup>3</sup>.3<sup>2</sup> |
+|  3 |      30  |           1,800 |           20 | 2<sup>3</sup>.3<sup>2</sup>.5<sup>2</sup> |
+|  4 |     210  |          88,200 |          237 | 2<sup>3</sup>.3<sup>2</sup>.5<sup>2</sup>.7<sup>2</sup> |
+|  5 |   2,310  |      10,672,200 |        3,268 | 2<sup>3</sup>.3<sup>2</sup>.5<sup>2</sup>.7<sup>2</sup>.11<sup>2</sup> |
+|  6 |  30,030  |   1,803,601,800 |       46,747 | 2<sup>3</sup>.3<sup>2</sup>.5<sup>2</sup>.7<sup>2</sup>.11<sup>2</sup>.13<sup>2</sup> |
+|  7 | 510,510  | 521,240,920,200 |      826,862 | 2<sup>3</sup>.3<sup>2</sup>.5<sup>2</sup>.7<sup>2</sup>.11<sup>2</sup>.13<sup>2</sup>.17<sup>2</sup> |
+
 # Challenge 2 - Kronecker Product
 
 ***Write a script to implement Kronecker Product on the given 2 matrices. e.g.***