Earliest difference between prime gaps: Difference between revisions

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Gap 276 starts at 649,580,171, gap 278 starts at 4,260,928,601, difference is 3,611,348,430.

</pre>

=={{header|Mathematica}}/{{header|Wolfram Language}}==

<lang Mathematica>primes = Prime[Range[10^7]];

gaps = {Differences[primes], Most[primes]} // Transpose;

tmp = GatherBy[gaps, First][[All, 1]];

tmp = SortBy[tmp, First];

starts = Association[Rule @@@ tmp];

set = {Most[tmp[[All, 1]]], Abs@Differences[tmp[[All, 2]]]} // Transpose;

data = Table[{n, k} = SelectFirst[set, Last/*GreaterThan[10^i]];

{10^i, n, starts[n], n + 2, starts[n + 2], k}, {i, 1, 7}];

StringTemplate["Earliest difference > `` between adjacent prime gap starting primes:

Gap `` starts at ``, gap `` starts at ``, difference is ``."]/*Print @@@ data;</lang>

<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 1831, difference is 1718.

Earliest difference > 1000 between adjacent prime gap starting primes:

Gap 14 starts at 113, gap 16 starts at 1831, difference is 1718.

Earliest difference > 10000 between adjacent prime gap starting primes:

Gap 36 starts at 9551, gap 38 starts at 30593, difference is 21042.

Earliest difference > 100000 between adjacent prime gap starting primes:

Gap 70 starts at 173359, gap 72 starts at 31397, difference is 141962.

Earliest difference > 1000000 between adjacent prime gap starting primes:

Gap 100 starts at 396733, gap 102 starts at 1444309, difference is 1047576.

Earliest difference > 10000000 between adjacent prime gap starting primes:

Gap 148 starts at 2010733, gap 150 starts at 13626257, difference is 11615524.</pre>

=={{header|Pascal}}==

==={{header|Free Pascal}}===