快速分解质因数

笔者在对素数的规律研究中,发现Sieve of Eratosthenes 方法对素数的筛选还是比较快的(参见拙作href="http://blog.csdn.net/northwolves/archive/2005/04/18/351998.aspx">http://blog.csdn.net/northwolves/archive/2005/04/18/351998.aspx</a>),将其应用于分解质因数,总体感觉还可以,代码如下:

'*******************************************************************************
' Target:to get all prime Factors of continuous numbers

'Author：northwolves

' Reference："Sieve of Eratosthenes"

'Createdate：2005-11-08 00:00:00

'*******************************************************************************

Function GetPrimeFactor(ByVal mynumber As Long, Optional counts As Long = 0) As String 'crash counts continuous number start by mynumber to prime factors

Dim max As Long, temp As Long, i As Long, p() As Long, scount As Long, s() As String, result() As String
scount = 0
max = Int(Sqr(mynumber + counts))

temp = 1
ReDim p(1 To temp) '
p(1) = 2

For i = 3 To max Step 2 ' skip those even number
sqrtmax = Int(Sqr(i)) + 1 'get the largest non-self factor of i
beprime = True ' init
For j = 1 To temp ' try all primer numbers we have found before.
If i Mod p(j) = 0 Then beprime = False: Exit For 'not a prime number
If p(j) > sqrtmax Then Exit For 'unless we'll waste our time
Next

If beprime = True Then ' then it is a prime number
temp = temp + 1 'add to it's count
ReDim Preserve p(1 To temp) 'define again
p(temp) = i
End If
Next

Dim number As Long
ReDim result(counts)
For temp = 0 To counts
number = mynumber + temp
result(temp) = number
scount = 0
For i = 1 To UBound(p)

again:
If number Mod p(i) = 0 Then
scount = scount + 1
ReDim Preserve s(1 To scount)
s(scount) = p(i)
number = number / p(i)
GoTo again
End If
If number = 1 Then Exit For
Next

If number > 1 Then
scount = scount + 1
ReDim Preserve s(1 To scount)
s(scount) = number
End If

If scount = 1 Then
result(temp) = result(temp) & " is a prime number"
Else
result(temp) = result(temp) & "=" & Join(s, "*")
End If

Next
GetPrimeFactor = Join(result, vbCrLf)
Erase p
Erase s
Erase result
End Function

Private Sub Command1_Click()
Debug.Print GetPrimeFactor(1234567800, 20)
End Sub

--------------------------------------------------------------------------------------------------

Return:

---------------------------------------------------------------------------------------------------

1234567800=2*2*2*3*3*5*5*47*14593
1234567801 is a prime number
1234567802=2*13*59*804803
1234567803=3*7*23*2556041
1234567804=2*2*1123*274837
1234567805=5*1249*197689
1234567806=2*3*293*702257
1234567807=11*19*5907023
1234567808=2*2*2*2*2*2*2*31*241*1291
1234567809=3*3*71*877*2203
1234567810=2*5*7*41*149*2887
1234567811 is a prime number
1234567812=2*2*3*17*6051803
1234567813=83*14874311
1234567814=2*617283907
1234567815=3*5*13*13*367*1327
1234567816=2*2*2*29*29*183497
1234567817=7*2081*84751
1234567818=2*3*3*3*3*3*11*230933
1234567819=107*11538017
1234567820=2*2*5*61728391
1234567821=3*411522607
1234567822=2*337*1831703
1234567823=4241*291103
1234567824=2*2*2*2*3*7*73*50333
1234567825=5*5*49382713
1234567826=2*19*23*37*38177
1234567827=3*3*113*1213931
1234567828=2*2*13*137*173297
1234567829=11*17*17*388351
1234567830=2*3*5*2797*14713
1234567831=7*176366833
1234567832=2*2*2*1153*133843
1234567833=3*179*757*3037
1234567834=2*587*1051591
1234567835=5*569*433943
1234567836=2*2*3*3*1993*17207
1234567837=61*139*145603
1234567838=2*7*7*1187*10613
1234567839=3*31*79*168037
1234567840=2*2*2*2*2*5*11*11*43*1483
1234567841=13*94966757
1234567842=2*3*131*1570697
1234567843=19813*62311
1234567844=2*2*101*1277*2393
1234567845=3*3*3*5*7*19*29*2371
1234567846=2*17*151*191*1259
1234567847=47*251*104651
1234567848=2*2*2*3*51440327
1234567849=23*53*1012771
1234567850=2*5*5*24691357
1234567851=3*11*41*912467
1234567852=2*2*7*521*84629
1234567853=1039*1188227
1234567854=2*3*3*13*229*23039
1234567855=5*6101*40471
1234567856=2*2*2*2*77160491
1234567857=3*1031*399149
1234567858=2*617283929
1234567859=7*1087*162251
1234567860=2*2*3*5*20576131
1234567861=59*89*235111
1234567862=2*11*67*257*3259
1234567863=3*3*17*37*218083
1234567864=2*2*2*19*8122157
1234567865=5*379*651487
1234567866=2*3*7*1459*20147
1234567867=13*94966759
1234567868=2*2*163*433*4373
1234567869=3*7499*54877
1234567870=2*5*31*31*128467
1234567871=271*4555601
1234567872=2*2*2*2*2*2*3*3*3*23*31063
1234567873=7*11*16033349
1234567874=2*29*167*197*647
1234567875=3*5*5*5*227*14503
1234567876=2*2*8689*35521
1234567877=181*6820817
1234567878=2*3*205761313
1234567879=20399*60521
1234567880=2*2*2*5*7*13*17*71*281
1234567881=3*3*137174209
1234567882=2*617283941
1234567883=19*43*1511099
1234567884=2*2*3*11*239*39133
1234567885=5*246913577
1234567886=2*593*1040951
1234567887=3*7*7*8398421
1234567888=2*2*2*2*97*103*7723
1234567889=127*487*19961
1234567890=2*3*3*5*3607*3803
1234567891 is a prime number
1234567892=2*2*41*7527853
1234567893=3*13*31655587
1234567894=2*7*47*479*3917
1234567895=5*11*23*975943
1234567896=2*2*2*3*83*619763
1234567897=17*73*994817
1234567898=2*61*10119409
1234567899=3*3*3*3*109*139831
1234567900=2*2*5*5*37*333667

1234567901=7*31*613*9281
1234567902=2*3*19*53*204331
1234567903=29*42571307
1234567904=2*2*2*2*2*38580247
1234567905=3*5*443*185789
1234567906=2*11*13*631*6841
1234567907 is a prime number
1234567908=2*2*3*3*7*4899079
1234567909=20887*59107
1234567910=2*5*123456791
1234567911=3*411522637
1234567912=2*2*2*317*486817
1234567913 is a prime number
1234567914=2*3*17*947*12781
1234567915=5*7*35273369
1234567916=2*2*499*618521
1234567917=3*3*11*223*55921
1234567918=2*23*79*339727
1234567919=13*94966763
1234567920=2*2*2*2*3*5*59*87187
1234567921=19*64977259
1234567922=2*7*88183423
1234567923=3*401*641*1601
1234567924=2*2*308641981
1234567925=5*5*193*255869
1234567926=2*3*3*3*43*107*4969
1234567927 is a prime number
1234567928=2*2*2*11*1709*8209
1234567929=3*7*67*827*1061
1234567930=2*5*157*786349
1234567931=17*72621643
1234567932=2*2*3*13*29*31*8803
1234567933=41*967*31139
1234567934=2*617283967
1234567935=3*3*5*27434843
1234567936=2*2*2*2*2*2*2*2*7*7*98419
1234567937=37*33366701
1234567938=2*3*205761323
1234567939=11*112233449
1234567940=2*2*5*19*113*28751
1234567941=3*23*47*199*1913
1234567942=2*18371*33601
1234567943=7*176366849
1234567944=2*2*2*3*3*17146777
1234567945=5*13*101*383*491
1234567946=2*617283973
1234567947=3*411522649
1234567948=2*2*17*277*65543
1234567949 is a prime number
1234567950=2*3*5*5*7*11*89*1201
1234567951=71*541*32141
1234567952=2*2*2*2*77160497
1234567953=3*3*3*45724739
1234567954=2*617283977
1234567955=5*53*1721*2707
1234567956=2*2*3*349*294787
1234567957=7*176366851
1234567958=2*13*307*154669
1234567959=3*19*61*149*2383
1234567960=2*2*2*5*30864199
1234567961=11*11*29*351829
1234567962=2*3*3*1663*41243
1234567963=31*173*211*1091
1234567964=2*2*7*23*659*2909
1234567965=3*5*17*137*35339
1234567966=2*617283983
1234567967 is a prime number
1234567968=2*2*2*2*2*3*269*47807
1234567969=43*28710883
1234567970=2*5*73*1691189
1234567971=3*3*7*13*397*3797
1234567972=2*2*11*359*78157
1234567973=131*283*33301
1234567974=2*3*37*41*135637
1234567975=5*5*233*211943
1234567976=2*2*2*139*1110223
1234567977=3*411522659
1234567978=2*7*19*809*5737
1234567979=59*59*83*4273
1234567980=2*2*3*3*3*3*5*769*991
1234567981 is a prime number
1234567982=2*17*36310823
1234567983=3*11*37411151
1234567984=2*2*2*2*13*13*456571
1234567985=5*7*7*97*51949
1234567986=2*3*205761331
1234567987=23*3533*15193
1234567988=2*2*47*6566851
1234567989=3*3*137174221
1234567990=2*5*29*4257131
1234567991=103*11986097
1234567992=2*2*2*3*7*311*23629
1234567993=1579*781867
1234567994=2*11*31*1810217
1234567995=3*5*82304533
1234567996=2*2*67*4606597
1234567997=13*19*79*151*419
1234567998=2*3*3*4691*14621
1234567999=7*17*2459*4219
1234568000=2*2*2*2*2*2*5*5*5*154321