Prime numbers whose neighboring pairs are tetraprimes: Difference between revisions
Prime numbers whose neighboring pairs are tetraprimes (view source)
Revision as of 21:03, 23 June 2023
, 11 months agoAdded FreeBasic
(→{{header|Wren}}: More efficient as we need to sort the gaps anyway to find the median.) |
(Added FreeBasic) |
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* OEIS sequence [[oeis:A362578|A362578: Prime numbers followed by two consecutive numbers which are products of four distinct primes (or tetraprimes).]]
<br>
=={{header|FreeBASIC}}==
{{trans|XPL0}}
<syntaxhighlight lang="vb">#include "isprime.bas"
Dim Shared As Boolean Have7 'A tetraprime factor is 7
Function isTetraprime(n As Integer) As Boolean
Dim As Boolean distinto
Dim As Integer div = 2, count = 0
While n >= div*div
distinto = True
While n Mod div = 0
If Not distinto Then Return False
distinto = False
count += 1
If div = 7 Then Have7 = True
n /= div
Wend
div += 1
Wend
If n > 1 Then count += 1
Return count = 4
End Function
Dim As Integer signo = -1
Dim As Integer TenPower = 1e5
Dim As Integer f, g, n, m, count, count7
Dim As Integer Gap, GapMin, GapMax, GapSum
For f = 5 To 7
For g = 1 To 2 'preceding or following neighboring pairs
count = 0
count7 = 0
m = 0
GapMin = -1
GapMax = 0
GapSum = 0
If f = 5 Then Print '100_000
For n = 3 To TenPower-1
If isPrime(n) Then
Have7 = False
If isTetraprime(n+1*signo) Then
If isTetraprime(n+2*signo) Then
count += 1
If f = 5 Then
Print Using "#######"; n;
If count Mod 10 = 0 Then Print
End If
If Have7 Then count7 += 1
If m <> 0 Then
Gap = n - m
If Gap <= GapMin Then GapMin = Gap
If Gap > GapMax Then GapMax = Gap
GapSum += Gap
End If
m = n
End If
End If
n += 1
End If
Next n
Print Using !"\nFound ##,### primes under ##,###,### whose preceding neighboring pair are tetraprimes"; count; TenPower
Print Using "of which #,### have a neighboring pair, one of whose factors is 7."; count7
Print Using !"\nMinimum gap between & primes : ##,###"; count; GapMin
Print Using "Average gap between & primes : ##,###"; count; (GapSum / (count-1))
Print Using "Maximum gap between & primes : ##,###"; count; GapMax
signo = signo * -1
Next g
TenPower *= 10
Next f
Sleep</syntaxhighlight>
{{out}}
<pre> 8647 15107 20407 20771 21491 23003 23531 24767 24971 27967
29147 33287 34847 36779 42187 42407 42667 43331 43991 46807
46867 51431 52691 52747 53891 54167 58567 63247 63367 69379
71711 73607 73867 74167 76507 76631 76847 80447 83591 84247
86243 87187 87803 89387 93887 97547 97847 98347 99431
Found 49 primes under 100,000 whose preceding neighboring pair are tetraprimes
of which 31 have a neighboring pair, one of whose factors is 7.
Minimum gap between 49 primes : 56
Average gap between 49 primes : 1,891
Maximum gap between 49 primes : 6,460
8293 16553 17389 18289 22153 26893 29209 33409 35509 36293
39233 39829 40493 41809 45589 48109 58393 59629 59753 59981
60493 60913 64013 64921 65713 66169 69221 71329 74093 75577
75853 77689 77933 79393 79609 82913 84533 85853 87589 87701
88681 91153 93889 96017 97381 98453
Found 46 primes under 100,000 whose preceding neighboring pair are tetraprimes
of which 36 have a neighboring pair, one of whose factors is 7.
Minimum gap between 46 primes : 112
Average gap between 46 primes : 2,004
Maximum gap between 46 primes : 10,284
Found 885 primes under 1,000,000 whose preceding neighboring pair are tetraprimes
of which 503 have a neighboring pair, one of whose factors is 7.
Minimum gap between 885 primes : 4
Average gap between 885 primes : 1,119
Maximum gap between 885 primes : 7,712
Found 866 primes under 1,000,000 whose preceding neighboring pair are tetraprimes
of which 492 have a neighboring pair, one of whose factors is 7.
Minimum gap between 866 primes : 4
Average gap between 866 primes : 1,146
Maximum gap between 866 primes : 10,284
Found 10,815 primes under 10,000,000 whose preceding neighboring pair are tetraprimes
of which 5,176 have a neighboring pair, one of whose factors is 7.
Minimum gap between 10815 primes : 4
Average gap between 10815 primes : 924
Maximum gap between 10815 primes : 9,352
Found 10,551 primes under 10,000,000 whose preceding neighboring pair are tetraprimes
of which 5,069 have a neighboring pair, one of whose factors is 7.
Minimum gap between 10551 primes : 4
Average gap between 10551 primes : 947
Maximum gap between 10551 primes : 10,284</pre>
=={{header|Wren}}==
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