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3:46

The larger templates are marginally faster (4 - 6%) but at great expense: 100's or 1000's of lines of code.

The macro assigned to my "Find Primes" button is listed below:

Option Explicit

Public i As Long

Public j As Long

Public estr As Double

Public esti As Long ' used with estr to estimate the size of the primes array

Public iend As Long ' user input - program will enumerate all prime <= iend

Public sr As Long ' square root of iend

Public PrX() As Boolean ' Templated Possible Primes

Public Primes() As Long ' # Primes <= iend

Sub DefinePrimes()

With ThisWorkbook.Worksheets("S

iend = .Cells(1, 5)

If iend < 40 Then

iend = 40

End If

estr = 1 / (WorksheetFunction.Ln(iend

esti = Int(estr * iend)

ReDim PrX(iend + 30) ' we always want to have a little extra space

ReDim Primes(esti) ' we always want to have a little extra space

sr = Sqr(iend)

.Cells(1, 4) = "Find Primes <= "

.Cells(1, 5) = iend

.Cells(2, 4) = "estr ="

.Cells(2, 5) = estr

.Cells(3, 4) = "esti ="

.Cells(3, 5) = esti

.Cells(4, 4) = "sr ="

.Cells(4, 5) = sr

PrX(2) = True

PrX(3) = True

PrX(5) = True

PrX(7) = True

i = 11

Do While i <= iend ' 2, 3 and 5 define the sieve template

PrX(i) = True ' I'll copy the template (7 x 11) 77 times

PrX(i + 2) = True ' turning potential primes "ON"

PrX(i + 6) = True

PrX(i + 8) = True

PrX(i + 12) = True

PrX(i + 18) = True

PrX(i + 20) = True

PrX(i + 26) = True

i = i + 30 ' 30 = 2 * 3 * 5 - size of template

Loop ' this section turned "On" all possible primes

For j = 7 To sr 'sr = floor(sqrt(iend))

If PrX(j) Then ' Turn off those that aren't prime

i = j * j

Do While i <= iend

PrX(i) = False

i = i + j + j ' j+j is a cycle or two faster than 2*j

Loop

End If

Next

j = 0 ' if still on, xfer index to list of primes

For i = 2 To iend

If PrX(i) Then

j = j + 1

If j <= esti And PrX(i) <> 0 Then

Primes(j) = i

End If

End If

Next

For i = 1 To j 'esti

.Cells(i, 1) = Primes(i)

Next

.Cells(5, 4) = "P Min ="

.Cells(5, 5) = 2

.Cells(6, 4) = "P Max ="

.Cells(6, 5) = Primes(j)

.Cells(7, 4) = "# Primes ="

.Cells(7, 5) = i - 1

End With

End Sub

Here is the XLSM file for Enumerating Prime Numbers Video::

(On sheet 5, I just found all 74,498 primes in the range [2..999983] in less than one second.)

https://filedb.experts-exchange.com/incoming/2017/03_w13/1153247/SieveTemplates.xlsm

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