Largest difference between adjacent primes

Largest difference between adjacent primes is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Task

Find and show on this page the largest difference between adjacent primes under 1,000,000.

Phix

Translation of: Wren

with javascript_semantics
atom t0 = time()
constant limit = iff(platform()=JS?1e8:1e9) - 1
sequence primes = get_primes_le(limit)
integer maxI = 0,
        maxDiff = 0
atom nextStop = 10
printf(1,"The largest differences between adjacent primes under the following limits is:\n")
for i=2 to length(primes) do
    integer diff = primes[i] - primes[i-1]
    if diff>maxDiff then
        maxDiff = diff
        maxI = i
    end if
    if i==length(primes) or primes[i+1]>nextStop then
        printf(1,"Under %,d: %,d - %,d = %,d\n", {nextStop, primes[maxI], primes[maxI-1], maxDiff})
        nextStop *= 10
    end if
end for
?elapsed(time()-t0)

Output:

The largest differences between adjacent primes under the following limits is:
Under 10: 5 - 3 = 2
Under 100: 97 - 89 = 8
Under 1,000: 907 - 887 = 20
Under 10,000: 9,587 - 9,551 = 36
Under 100,000: 31,469 - 31,397 = 72
Under 1,000,000: 492,227 - 492,113 = 114
Under 10,000,000: 4,652,507 - 4,652,353 = 154
Under 100,000,000: 47,326,913 - 47,326,693 = 220
Under 1,000,000,000: 436,273,291 - 436,273,009 = 282
"12.7s"

Almost all the time is spent constructing the list of primes. It is about 4 times slower under pwa/p2js so limited to 1e8 when running in a browser to keep the time below 5s instead of over 50s.

Raku

Built-ins

<lang perl6>for 2..8 -> $n {

   printf "Largest prime gap up to {10 ** $n}: %d - between %d and %d.\n", .[0], |.[1]
     given max (^10**$n).grep(&is-prime).rotor(2=>-1).map({.[1]-.[0],$_})

}</lang>

Output:

Largest prime gap up to 100: 8 - between 89 and 97.
Largest prime gap up to 1000: 20 - between 887 and 907.
Largest prime gap up to 10000: 36 - between 9551 and 9587.
Largest prime gap up to 100000: 72 - between 31397 and 31469.
Largest prime gap up to 1000000: 114 - between 492113 and 492227.
Largest prime gap up to 10000000: 154 - between 4652353 and 4652507.
Largest prime gap up to 100000000: 220 - between 47326693 and 47326913.

Or, significantly faster using a

Module

<lang perl6>use Math::Primesieve; my $sieve = Math::Primesieve.new;

for 2..8 -> $n {

   printf "Largest prime gap up to {10 ** $n}: %d - between %d and %d.\n", .[0], |.[1]
     given max $sieve.primes(10 ** $n).rotor(2=>-1).map({.[1]-.[0],$_})

}</lang> Same output

Ring

<lang ring> load "stdlib.ring" see "working..." + nl limit = 1000000 Primes = [] maxOld = 0 newDiff = 0 oldDiff = 0

for n = 1 to limit

   newDiff = n - maxOld
   if isprime(n) 
      if newDiff > oldDiff
         add(Primes,[n,maxOld])
         oldDiff = newDiff
      ok
      maxOld = n
   ok

next

len = len(Primes) diff = Primes[len][1] - Primes[len][2] see Primes[len(Primes)] see nl + "Largest difference is = " + diff + nl see "done..." + nl </lang>

Output:

working...
492227
492113
Largest difference is = 114
done...

Wren

Library: Wren-math

Library: Wren-fmt

<lang ecmascript>import "./math" for Int, Nums import "/fmt" for Fmt

var limit = 1e9 - 1 var primes = Int.primeSieve(limit) var maxI = 0 var maxDiff = 0 var nextStop = 10 System.print("The largest differences between adjacent primes under the following limits is:") for (i in 1...primes.count) {

   var diff = primes[i] - primes[i-1]
   if (diff > maxDiff) {
       maxDiff = diff
       maxI = i
   }
   if (i == primes.count - 1 || primes[i+1] > nextStop)  {
       Fmt.print("Under $,d: $,d - $,d = $,d", nextStop, primes[maxI], primes[maxI-1], maxDiff)
       nextStop = nextStop * 10
   }

}</lang>

Output:

The largest differences between adjacent primes under the following limits is:
Under 10: 5 - 3 = 2
Under 100: 97 - 89 = 8
Under 1,000: 907 - 887 = 20
Under 10,000: 9,587 - 9,551 = 36
Under 100,000: 31,469 - 31,397 = 72
Under 1,000,000: 492,227 - 492,113 = 114
Under 10,000,000: 4,652,507 - 4,652,353 = 154
Under 100,000,000: 47,326,913 - 47,326,693 = 220
Under 1,000,000,000: 436,273,291 - 436,273,009 = 282