Five Consecutive Primes starting from M1 create two palindromic numbers:
M1*M2*...*M5 = Pal1
M1^2+M2^2+...M5^2 =Pal2
Find M1, Pal1 & Pal2.
I know only one solution...
DefDbl A-Z
Dim crlf$
Private Sub Form_Load()
Text1.Text = ""
crlf$ = Chr(13) + Chr(10)
Form1.Visible = True
a = 2: b = 3: c = 5: d = 7: e = 11
prod = a * b * c * d * e
Do
If isPalin(prod) Then
tot = a * a + b * b + c * c + d * d + e * e
If isPalin(tot) Then
Text1.Text = Text1.Text & a & Str(b) & Str(c) & Str(d) & Str(e) & " " & Str(prod) & Str(tot) & crlf
done = 1
End If
End If
DoEvents
f = nxtprm(e)
a = b: b = c: c = d: d = e: e = f
prod = a * b * c * d * e
Loop Until prod > 1E+15
Text1.Text = Text1.Text & crlf & a & Str(prod) & " done "
End Sub
Function isPalin(n)
s$ = Format$(n, "###############")
good = 1
For i = 1 To Len(s$) / 2
If Mid$(s$, i, 1) <> Mid$(s$, Len(s$) + 1 - i, 1) Then good = 0: Exit For
Next
isPalin = good
End Function
Function prmdiv(num)
Dim n, dv, q
If num = 1 Then prmdiv = 1: Exit Function
n = Abs(num): If n > 0 Then limit = Sqr(n) Else limit = 0
If limit <> Int(limit) Then limit = Int(limit + 1)
dv = 2: GoSub DivideIt
dv = 3: GoSub DivideIt
dv = 5: GoSub DivideIt
dv = 7
Do Until dv > limit
GoSub DivideIt: dv = dv + 4 '11
GoSub DivideIt: dv = dv + 2 '13
GoSub DivideIt: dv = dv + 4 '17
GoSub DivideIt: dv = dv + 2 '19
GoSub DivideIt: dv = dv + 4 '23
GoSub DivideIt: dv = dv + 6 '29
GoSub DivideIt: dv = dv + 2 '31
GoSub DivideIt: dv = dv + 6 '37
Loop
If n > 1 Then prmdiv = n
Exit Function
DivideIt:
Do
q = Int(n / dv)
If q * dv = n And n > 0 Then
prmdiv = dv: Exit Function
Else
Exit Do
End If
Loop
Return
End Function
Function nxtprm(x)
Dim n
n = x + 1
While prmdiv(n) < n Or n < 2
n = n + 1
Wend
nxtprm = n
End Function
finds
7 11 13 17 19 323323 989
991 1.02906689782902E+15 done
meaning M1 is 7, Pal1 is 323323 and Pal2 is 989. Checking for further answers stopped at the prime 991 as the product became over 10^15, beyond the reliable accuracy of VB.
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Posted by Charlie
on 2018-08-11 13:42:49 |
computer solution
