Type PrimeGaps
    As Ulong lastPrime
    As Ulongint gapStarts(1 To 1e7)
End Type

Function NextPrime(n As Ulong) As Ulong
    Dim As Ulong j, i = n + 1
    Do
        For j = 2 To Sqr(i)
            If i Mod j = 0 Then Exit For
        Next j
        If j > Sqr(i) Then Return i
        i += 1
    Loop
End Function

Function findGapStart(Byref pg As PrimeGaps, gap As Ulongint) As Ulongint
    Dim As Ulongint prev, diff
    If pg.gapStarts(gap) <> 0 Then Return pg.gapStarts(gap)
    Do
        prev = pg.lastPrime
        pg.lastPrime = NextPrime(pg.lastPrime)
        diff = pg.lastPrime - prev
        pg.gapStarts(diff) = prev
        If gap = diff Then Return prev
    Loop
End Function

Dim Shared As PrimeGaps pg
pg.lastPrime = NextPrime(2)
Dim As Ulongint limit = 1e7
Dim As Integer pm = 10
Dim As Ulongint start1, start2, gap1 = 2, gap2, diff
Do
    start1 = findGapStart(pg, gap1)
    gap2 = gap1 + 2
    start2 = findGapStart(pg, gap2)
    diff = Abs(start2 - start1)
    If diff > pm Then
        Print "Earliest difference >"; pm; " between adjacent prime gap starting primes:"
        Print "Gap "; gap1; " starts at "; start1; ", gap "; gap2; " starts at "; start2; ", difference is "; diff; !".\n"
        If pm = limit Then Exit Do
        pm *= 10
    Else
        gap1 = gap2
    End If
Loop

Sleep