Earliest difference between prime gaps: Difference between revisions
Earliest difference between prime gaps (view source)
Revision as of 13:55, 22 November 2021
, 2 years agoAdded Java solution
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Note: the earliest value found for each order of magnitude may not be unique, in fact, ''is'' not unique; also, with the gaps in ascending order, the minimal starting values are not strictly ascending.
=={{header|Java}}==
Uses the PrimeGenerator class from [[Extensible prime generator#Java]].
<lang java>import java.util.HashMap;
import java.util.Map;
public class PrimeGaps {
private Map<Integer, Integer> gapStarts = new HashMap<>();
int lastPrime;
PrimeGenerator primeGenerator = new PrimeGenerator(1000, 500000);
public static void main(String[] args) {
final int limit = 100000000;
PrimeGaps pg = new PrimeGaps();
for (int pm = 10, gap1 = 2;;) {
int start1 = pg.findGapStart(gap1);
int gap2 = gap1 + 2;
int start2 = pg.findGapStart(gap2);
int diff = start2 > start1 ? start2 - start1 : start1 - start2;
if (diff > pm) {
System.out.printf(
"Earliest difference > %,d between adjacent prime gap starting primes:\n"
+ "Gap %,d starts at %,d, gap %,d starts at %,d, difference is %,d.\n\n",
pm, gap1, start1, gap2, start2, diff);
if (pm == limit)
break;
pm *= 10;
} else {
gap1 = gap2;
}
}
}
private int findGapStart(int gap) {
Integer start = gapStarts.get(gap);
if (start != null)
return start;
for (;;) {
int prev = lastPrime;
lastPrime = primeGenerator.nextPrime();
int diff = lastPrime - prev;
gapStarts.putIfAbsent(diff, prev);
if (diff == gap)
return prev;
}
}
}</lang>
{{out}}
<pre>
Earliest difference > 10 between adjacent prime gap starting primes:
Gap 4 starts at 7, gap 6 starts at 23, difference is 16.
Earliest difference > 100 between adjacent prime gap starting primes:
Gap 14 starts at 113, gap 16 starts at 1,831, difference is 1,718.
Earliest difference > 1,000 between adjacent prime gap starting primes:
Gap 14 starts at 113, gap 16 starts at 1,831, difference is 1,718.
Earliest difference > 10,000 between adjacent prime gap starting primes:
Gap 36 starts at 9,551, gap 38 starts at 30,593, difference is 21,042.
Earliest difference > 100,000 between adjacent prime gap starting primes:
Gap 70 starts at 173,359, gap 72 starts at 31,397, difference is 141,962.
Earliest difference > 1,000,000 between adjacent prime gap starting primes:
Gap 100 starts at 396,733, gap 102 starts at 1,444,309, difference is 1,047,576.
Earliest difference > 10,000,000 between adjacent prime gap starting primes:
Gap 148 starts at 2,010,733, gap 150 starts at 13,626,257, difference is 11,615,524.
Earliest difference > 100,000,000 between adjacent prime gap starting primes:
Gap 198 starts at 46,006,769, gap 200 starts at 378,043,979, difference is 332,037,210.
</pre>
=={{header|Julia}}==
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