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1、 . . . .VB循环程序例题附答案 1.素数1. 100,999范围内同时满足以下两个条件的十进制数. 其个位数字与十位数字之和除以10所得的余数是百位数字;该数是素数; 求有多少个这样的数? 15n = 0For i = 100 To 999a = i 100b = i 10 Mod 10c = i Mod 10If (c + b) Mod 10 = a Then x = 0 For j = 2 To i - 1 If i Mod j = 0 Then x = 1: Exit For Next j If x = 0 Then n = n + 1End IfNext iPrint n2.
2、300,800范围内同时满足以下两个条件的十进制数. 其个位数字与十位数字之和除以10所得的余数是百位数字 ;该数是素数;求满足上述条件的最大的三位十进制数。761For i = 300 To 800a = i 100b = i 10 Mod 10c = i Mod 10If (c + b) Mod 10 = a Then x = 0 For j = 2 To i - 1 If i Mod j = 0 Then x = 1: Exit For Next j If x = 0 Then s = iEnd IfNext iPrint s3. 除1和它本身外,不能被其它整数整除的正整数称为素数(注:
3、1不是素数,2是素数)。若两素数之差为2 ,则称两素数为双胞胎数,问31,601之间有多少对双胞胎数。22n = 0For i = 31 To 601 - 2 x = 0 For j = 2 To Sqr(i) If i Mod j = 0 Then x = 1: Exit For Next j If x = 0 Then y = 0 For j = 2 To Sqr(i + 2) If (i + 2) Mod j = 0 Then y = 1: Exit For Next j If y = 0 Then n = n + 1 End IfNext iPrint n4.数学家哥德巴赫曾猜测:任何
4、大于6的偶数都可以分解成两个素数(素数对)的和。但有些偶数可以分解成多种素数对的和,如: 10=3+7,10=5+5,即10可以分解成两种不同的素数对。试求6744可以分解成多少种不同的素数对(注: A+B与B+A认为是相同素数对)144n = 0For i = 2 To 6744 / 2 x = 0 For j = 2 To Sqr(i) If i Mod j = 0 Then x = 1: Exit For Next j If x = 0 Then y = 0 For j = 2 To Sqr(6744 - i) If (6744 - i) Mod j = 0 Then y = 1: Ex
5、it For Next j If y = 0 Then n = n + 1 End IfNext iPrint n5. 两个素数之差为2,则称这两个素数为双胞胎数。求出200,1000之间的最大一对双胞胎数的和。1764For i = 200 To 1000 - 2 x = 0 For j = 2 To Sqr(i) If i Mod j = 0 Then x = 1: Exit For Next j If x = 0 Then y = 0 For j = 2 To Sqr(i + 2) If (i + 2) Mod j = 0 Then y = 1: Exit For Next j If y
6、 = 0 Then s = i + i + 2 End IfNext iPrint s6. 一个素数(设为p)依次从最高位去掉一位,二位,三位,若得到的各数仍都是素数(注:除1和它本身外,不能被其它整数整除的正整数称为素数,1不是素数,2是素数),且数p的各位数字均不为零,则称该数p为逆向超级素数。例如,617,17,7都是素数,因此617是逆向超级素数,尽管503,03,3都是素数,但它不是逆向超级素数,因为它包含有零。试求100,999之内的所有逆向超级素数的个数。 39n = 0For i = 100 To 999 a = i 10 Mod 10 b = i Mod 10 If a 0
7、And b 0 And b 1 Then x = 0 For j = 2 To Sqr(i) If i Mod j = 0 Then x = 1: Exit For Next j If x = 0 Then y = 0 c = i Mod 100 For j = 2 To Sqr(c) If c Mod j = 0 Then y = 1: Exit For Next j If y = 0 Then z = 0 For j = 2 To Sqr(b) If b Mod j = 0 Then z = 1: Exit For Next j If z = 0 Then n = n + 1 End If
8、 End If End IfNext iPrint n7.德国数学家哥德巴赫曾猜测:任何大于6的偶数都可以分解成两个素数(素数对)的和。但有些偶数可以分解成多种素数对的和,如: 10=3+7,10=5+5,即10可以分解成两种不同的素数对。试求1234可以分解成多少种不同的素数对(注: A+B与B+A认为是相同素数对)25n = 0For i = 2 To 1234 / 2 x = 0 For j = 2 To Sqr(i) If i Mod j = 0 Then x = 1: Exit For Next j If x = 0 Then y = 0 For j = 2 To Sqr(1234
9、- i) If (1234 - i) Mod j = 0 Then y = 1: Exit For Next j If y = 0 Then n = n + 1 End IfNext iPrint n8.求100,900之间相差为12的素数对(注:要求素数对的两个素数均在该范围内)的个数。50n = 0For i = 100 To 900 - 12 x = 0 For j = 2 To Sqr(i) If i Mod j = 0 Then x = 1: Exit For Next j If x = 0 Then y = 0 For j = 2 To Sqr(i + 12) If (i + 12
10、) Mod j = 0 Then y = 1: Exit For Next j If y = 0 Then n = n + 1 End IfNext iPrint n9.一个素数(设为p)依次从最高位去掉一位,二位,三位,若得到的各数仍都是素数(注:1不是素数),且数p的各位数字均不为零,则称该数p为逆向超级素数。例如,617,17,7都是素数,因此617是逆向超级素数,但尽管503,03,3都是素数,但它不是逆向超级素数,因为它包含有零。试求100,999之内的所有逆向超级素数的和。21645s = 0For i = 100 To 999 a = i 10 Mod 10 b = i Mod
11、10 If a 0 And b 0 And b 1 Then x = 0 For j = 2 To Sqr(i) If i Mod j = 0 Then x = 1: Exit For Next j If x = 0 Then y = 0 c = i Mod 100 For j = 2 To Sqr(c) If c Mod j = 0 Then y = 1: Exit For Next j If y = 0 Then z = 0 For j = 2 To Sqr(b) If b Mod j = 0 Then z = 1: Exit For Next j If z = 0 Then s = s
12、+ i End If End If End IfNext iPrint s10.一个素数(设为p)依次从最高位去掉一位,二位,三位,若得到的各数仍都是素数(注:1不是素数,2是素数),且数p的各位数字均不为零,则称该数p为逆向超级素数。例如,617,17,7都是素数,因此617是逆向超级素数,但尽管503,03,3都是素数,但它不是逆向超级素数,因为它包含有零。试求100,999之内的所有逆向超级素数从大到小数的第10个素数是多少?797n = 0For i = 999 To 100 Step -1 a = i 10 Mod 10 b = i Mod 10 If a 0 And b 0 And
13、 b 1 Then x = 0 For j = 2 To Sqr(i) If i Mod j = 0 Then x = 1: Exit For Next j If x = 0 Then y = 0 c = i Mod 100 For j = 2 To Sqr(c) If c Mod j = 0 Then y = 1: Exit For Next j If y = 0 Then z = 0 For j = 2 To Sqr(b) If b Mod j = 0 Then z = 1: Exit For Next j If z = 0 Then n = n + 1: If n = 10 Then s = i End If End If End IfNext iPrint s11.一个自然数是素数,且它的数字位置经过任意对