How to resolve the algorithm Truncatable primes step by step in the FreeBASIC programming language
Published on 12 May 2024 09:40 PM
How to resolve the algorithm Truncatable primes step by step in the FreeBASIC programming language
Table of Contents
Problem Statement
A truncatable prime is a prime number that when you successively remove digits from one end of the prime, you are left with a new prime number.
The number 997 is called a left-truncatable prime as the numbers 997, 97, and 7 are all prime. The number 7393 is a right-truncatable prime as the numbers 7393, 739, 73, and 7 formed by removing digits from its right are also prime. No zeroes are allowed in truncatable primes.
The task is to find the largest left-truncatable and right-truncatable primes less than one million (base 10 is implied).
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Truncatable primes step by step in the FreeBASIC programming language
Source code in the freebasic programming language
' FB 1.05.0 Win64
Function isPrime(n As Integer) As Boolean
If n Mod 2 = 0 Then Return n = 2
If n Mod 3 = 0 Then Return n = 3
Dim d As Integer = 5
While d * d <= n
If n Mod d = 0 Then Return False
d += 2
If n Mod d = 0 Then Return False
d += 4
Wend
Return True
End Function
Dim As UInteger i, j, p, pow, lMax = 2, rMax = 2
Dim s As String
' largest left truncatable prime less than 1000000
' It can't end with 1, 4, 6, 8 or 9 as these numbers are not prime
' Nor can it end in 2 if it has more than one digit as such a number would divide by 2
For i = 3 To 999997 Step 2
s = Str(i)
If Instr(s, "0") > 1 Then Continue For '' cannot contain 0
j = s[Len(s) - 1] - 48
If j = 1 OrElse j = 9 Then Continue For
p = i
pow = 10 ^ (Len(s) - 1)
While pow > 1
If Not isPrime(p) Then Continue For
p Mod= pow
pow \= 10
Wend
lMax = i
Next
' largest right truncatable prime less than 1000000
' It can't begin with 1, 4, 6, 8 or 9 as these numbers are not prime
For i = 3 To 799999 Step 2
s = Str(i)
If Instr(s, "0") > 1 Then Continue For '' cannot contain 0
j = s[0] - 48
If j = 1 OrElse j = 4 OrElse j = 6 Then Continue For
p = i
While p > 0
If Not isPrime(p) Then Continue For
p \= 10
Wend
rMax = i
Next
Print "Largest left truncatable prime : "; lMax
Print "Largest right truncatable prime : "; rMax
Print
Print "Press any key to quit"
Sleep
' version 10-12-2016
' compile with: fbc -s console
Dim Shared As Byte isPrime()
Sub sieve(m As UInteger)
Dim As Integer i, j
ReDim isPrime(m)
For i = 4 To m Step 2
isPrime(i) = 1
Next
For i = 3 To Sqr(m) Step 2
If isPrime(i) = 0 Then
For j = i * i To m Step i * 2
isPrime(j) = 1
Next
End If
Next
End Sub
' ------=< MAIN >=------
#Define max 1000000 'upto 2^30 max for 32bit OS
Dim As UInteger a(), lt_prime(5000), rt_prime(100)
Dim As UInteger i, j, j1, p1, p2, left_max, right_max
sieve(max)
' left truncatable primes
' if odd and ends with 3 or 7, never ends 1 or 9 (no prime
' never ends on a 2 or 5 and starts with 1 to 9
lt_prime(1) = 3 : lt_prime(2) = 7
p1 = 1 : p2 = 2
Do
For i = 1 To 9
j = Val( Str(i) + Str(lt_prime(p1)) )
If j > max Then Exit Do
If isPrime(j) = 0 Then ' if prime then add to the list
p2 += 1
lt_prime(p2) = j
If Left_max < j Then left_max = j
End If
Next
p1 += 1
Loop Until p1 > p2 ' no more numbers to process
' right truncatable prime
' start with 2, 3, 5 or 7 and end with 1, 3, 7 or 9
rt_prime(1) = 2 : rt_prime(2) = 3 : rt_prime(3) = 5 : rt_prime(4) = 7
p1 = 1 : p2 = 4
Dim As UInteger end_num(1 To 4) => {1, 3, 7, 9}
Do
j1 = rt_prime(p1) * 10
If j1 > max Then Exit Do
For i = 1 To 4
j = j1 + End_num(i)
If isprime(j) = 0 Then ' if prime then add to the list
p2 += 1
rt_prime(p2) = j
' If right_max < j Then right_max = j
End If
Next
p1 += 1
Loop Until p1 > p2 ' no more numbers to process
' the last one added is the biggest
right_max = rt_prime(p2)
Print
Print "The biggest left truncatable prime below"; max; " is "; left_max
Print "The biggest right truncatable prime below"; max; " is "; right_max
' empty keyboard buffer
While Inkey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End
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