Primes whose first and last number is 3: Difference between revisions

===Basic task===

</pre>

===More general===

This version deals with primes (in base 10) beginning and ending with any specified digit and with up to a given number of digits.

<lang ecmascript>import "/math" for Int

import "/trait" for Stepped

import "/seq" for Lst

import "/fmt" for Fmt

var getQualifyingPrimes = Fn.new { |x, d|

if (d.type != Num || !d.isInteger || d < 1) Fiber.abort("Invalid number of digits.")

if (x == 2 || x == 5) return [x]

if (x % 2 == 0) return []

var primes = []

var candidates = [x]

for (i in 1...d) {

var pow = 10.pow(i)

var start = x * (pow + 1)

var end = start + pow - 10

candidates.addAll(Stepped.new(start..end, 10).toList)

}

return candidates.where { |cand| Int.isPrime(cand) }.toList

}

var d = 4 // up to 'd' digits

for (x in [1, 2, 3, 5, 7, 9]) { // begins and ends with 'x'

var primes = getQualifyingPrimes.call(x, d)

var len = d + (d/3).floor

Fmt.print("Primes under $,%(len)d which begin and end in $d:", 10.pow(d), x)

for (chunk in Lst.chunks(primes, 10)) Fmt.print("$,%(len)d", chunk)

System.print("\nFound %(primes.count) such primes.\n")

}</lang>

{{out}}

<pre>

Primes under 10,000 which begin and end in 1:

11 101 131 151 181 191 1,021 1,031 1,051 1,061

1,091 1,151 1,171 1,181 1,201 1,231 1,291 1,301 1,321 1,361

1,381 1,451 1,471 1,481 1,511 1,531 1,571 1,601 1,621 1,721

1,741 1,801 1,811 1,831 1,861 1,871 1,901 1,931 1,951

Found 39 such primes.

Primes under 10,000 which begin and end in 2:

2

Found 1 such primes.

Primes under 10,000 which begin and end in 3:

3 313 353 373 383 3,023 3,083 3,163 3,203 3,253

3,313 3,323 3,343 3,373 3,413 3,433 3,463 3,533 3,583 3,593

3,613 3,623 3,643 3,673 3,733 3,793 3,803 3,823 3,833 3,853

3,863 3,923 3,943

Found 33 such primes.

Primes under 10,000 which begin and end in 5:

5

Found 1 such primes.

Primes under 10,000 which begin and end in 7:

7 727 757 787 797 7,027 7,057 7,127 7,177 7,187

7,207 7,237 7,247 7,297 7,307 7,417 7,457 7,477 7,487 7,507

7,517 7,537 7,547 7,577 7,607 7,687 7,717 7,727 7,757 7,817

7,867 7,877 7,907 7,927 7,937

Found 35 such primes.

Primes under 10,000 which begin and end in 9:

919 929 9,029 9,049 9,059 9,109 9,199 9,209 9,239 9,319

9,349 9,419 9,439 9,479 9,539 9,619 9,629 9,649 9,679 9,689

9,719 9,739 9,749 9,769 9,829 9,839 9,859 9,929 9,949

Found 29 such primes.