Earliest difference between prime gaps: Difference between revisions
Earliest difference between prime gaps (view source)
Revision as of 19:26, 20 November 2021
, 2 years agoAdded Wren
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Earliest difference > 1,000,000,000 between adjacent prime gap starting primes:
Gap 276 starts at 649,580,171, gap 278 starts at 4,260,928,601, difference is 3,611,348,430</pre>
=={{header|Wren}}==
{{libheader|Wren-math}}
{{libheader|Wren-fmt}}
Judging by the Raku solution, I've assumed that it's the ''absolute value'' of the difference that is to be tested. If not, for the earliest ''positive'' difference > 100,000, we'd have:
Gap 72 starts at 31,397, gap 74 starts at 404,597, difference is 373,200.
Unfortunately, my machine doesn't have enough memory to look for the earliest difference > 1 billion.
<lang ecmascript>import "./math" for Int
import "/fmt" for Fmt
var limit = 1e8
var gapStarts = {}
var primes = Int.primeSieve(limit * 4)
for (i in 1...primes.count) {
var gap = primes[i] - primes[i-1]
if (!gapStarts[gap]) gapStarts[gap] = primes[i-1]
}
var pm = 10
var gap1 = 2
while (true) {
while (!gapStarts[gap1]) gap1 = gap1 + 2
var start1 = gapStarts[gap1]
var gap2 = gap1 + 2
if (!gapStarts[gap2]) {
gap1 = gap2 + 2
continue
}
var start2 = gapStarts[gap2]
var diff = (start2 - start1).abs
if (diff > pm) {
Fmt.print("Earliest difference > $,d between adjacent prime gap starting primes:", pm)
Fmt.print("Gap $d starts at $,d, gap $d starts at $,d, difference is $,d.\n", gap1, start1, gap2, start2, diff)
if (pm == limit) break
pm = pm * 10
} else {
gap1 = gap2
}
}</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>
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