# Substring primes

Generic solution for any base >= 2.

```ruby
func split_at_indices(array, indices) {
 
    var parts = []
    var i = 0
 
    for j in (indices) {
        parts << [array[i..j]]
        i = j+1
    }
 
    parts
}
 
func consecutive_partitions(array, callback) {
    for k in (0..array.len) {
        combinations(array.len, k, {|*indices|
            var t = split_at_indices(array, indices)
            if (t.sum_by{.len} == array.len) {
                callback(t)
            }
        })
    }
}
 
func is_substring_prime(digits, base) {
 
    for k in (^digits) {
        digits.first(k+1).digits2num(base).is_prime || return false
    }
 
    consecutive_partitions(digits, {|part|
        part.all { .digits2num(base).is_prime } || return false
    })
 
    return true
}
 
func generate_from_prefix(p, base, digits) {
 
    var seq = [p]
 
    for d in (digits) {
        var t = [d, p...]
        if (is_prime(t.digits2num(base)) && is_substring_prime(t, base)) {
            seq << __FUNC__(t, base, digits)...
        }
    }
 
    return seq
}
 
func substring_primes(base) {     # finite sequence for each base >= 2
 
    var prime_digits = (base-1 -> primes)   # prime digits < base
 
    prime_digits.map  {|p| generate_from_prefix([p], base, prime_digits)... }\
                .map  {|t| digits2num(t, base) }\
                .sort
}
 
for base in (2..20) {
    say "base = #{base}: #{substring_primes(base)}"
}
```

#### Output:

```
base = 2: []
base = 3: [2]
base = 4: [2, 3, 11]
base = 5: [2, 3, 13, 17, 67]
base = 6: [2, 3, 5, 17, 23]
base = 7: [2, 3, 5, 17, 19, 23, 37]
base = 8: [2, 3, 5, 7, 19, 23, 29, 31, 43, 47, 59, 61, 157, 239, 251, 349, 379, 479, 491]
base = 9: [2, 3, 5, 7, 23, 29, 47]
base = 10: [2, 3, 5, 7, 23, 37, 53, 73, 373]
base = 11: [2, 3, 5, 7, 29, 79]
base = 12: [2, 3, 5, 7, 11, 29, 31, 41, 43, 47, 67, 71, 89, 137, 139, 359, 499, 503, 521, 569, 571, 809, 857, 859, 6043]
base = 13: [2, 3, 5, 7, 11, 29, 31, 37, 41, 67, 379]
base = 14: [2, 3, 5, 7, 11, 13, 31, 41, 47, 53, 73, 83, 101, 103, 109, 157, 167, 193, 439, 661, 1033, 2203]
base = 15: [2, 3, 5, 7, 11, 13, 37, 41, 43, 47, 107, 167, 197, 557, 617, 647]
base = 16: [2, 3, 5, 7, 11, 13, 37, 43, 53, 59, 61, 83, 179, 181, 211, 691, 947, 3389]
base = 17: [2, 3, 5, 7, 11, 13, 37, 41, 47, 53, 223, 631]
base = 18: [2, 3, 5, 7, 11, 13, 17, 41, 43, 47, 53, 59, 61, 67, 71, 97, 101, 103, 107, 131, 137, 139, 211, 239, 241, 251, 311, 313, 317, 751, 787, 859, 1069, 1103, 1109, 1213, 1223, 1283, 1289, 1759, 1831, 1861, 1871, 1931, 1933, 2371, 3803, 4349, 4523, 5639, 5647, 15467, 19867, 34807]
base = 19: [2, 3, 5, 7, 11, 13, 17, 41, 43, 59, 97, 211]
base = 20: [2, 3, 5, 7, 11, 13, 17, 19, 43, 47, 53, 59, 67, 71, 73, 79, 103, 107, 113, 151, 157, 223, 227, 233, 239, 263, 271, 277, 347, 353, 359, 383, 397, 1063, 1423, 1427, 1433, 1439, 1471, 1583, 1597, 3023, 4663, 4783, 5273, 5279, 7673, 28663]
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://trizen.gitbook.io/sidef-lang/programming_tasks/s/substring_primes.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.