Largest difference between adjacent primes
Find and show on this page the largest difference between adjacent primes under 1,000,000.
- Task
C
<lang c>#include<stdio.h>
- include<stdlib.h>
int isprime( int p ) {
int i;
if(p==2) return 1;
if(!(p%2)) return 0;
for(i=3; i*i<=p; i+=2) {
if(!(p%i)) return 0;
}
return 1;
}
int nextprime( int p ) {
int i=0; if(p==0) return 2; if(p<3) return p+1; while(!isprime(++i + p)); return i+p;
}
int main(void) {
int i=3, j=5, champ=3, champj=5, record=2;
for(i=3;j<=1000000;i=j) {
j=nextprime(i);
if(j-i>record) {
champ=i;
champj=j;
record = j-i;
}
}
printf( "The largest difference was %d, between %d and %d.\n", record, champ, champj );
return 0;
}</lang>
- Output:
The largest difference was 114, between 492113 and 492227.
FreeBASIC
<lang freebasic>#include "isprime.bas"
function nextprime( n as uinteger ) as uinteger
'finds the next prime after n
if n = 0 then return 2
if n < 3 then return n + 1
dim as integer q = n + 2
while not isprime(q)
q+=2
wend
return q
end function
dim as uinteger i = 5, j, champ=3, champj=5, record=2 while i<1000000
j = nextprime(i)
if j-i > record then
champ = i
champj = j
record = j - i
end if
i = j
wend
print using "The largest difference was ####, between ####### and #######";record;champ;champj</lang>
- Output:
The largest difference was 114 between 492113 and 492227
GW-BASIC
<lang gwbasic>10 R=2 : P=3 : P2=0 20 GOSUB 190 30 IF P2>1000000! THEN GOTO 70 40 IF P2-P > R THEN GOSUB 270 50 P=P2 60 GOTO 20 70 PRINT "The biggest difference was ";R;", between ";C1;" and ";C2 80 END 90 REM tests if a number is prime 100 Q=0 110 IF P = 2 THEN Q = 1:RETURN 120 IF P=3 THEN Q=1:RETURN 130 I=1 140 I=I+1 150 IF INT(P/I)*I = P THEN RETURN 160 IF I*I<=P THEN GOTO 140 170 Q = 1 180 RETURN 190 REM finds the next prime after P, result in P2 200 IF P = 0 THEN P2 = 2: RETURN 210 IF P<3 THEN P2 = P + 1: RETURN 220 T = P 230 P = P + 1 240 GOSUB 90 250 IF Q = 1 THEN P2 = P: P = T: RETURN 260 GOTO 230 270 C1=P 280 C2 = P2 290 R = P2 - P 300 RETURN</lang>
Phix
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
<lang ecmascript>import "./math" for Int 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