## King 4 years ago :Help...........for how many positive integers n is n^3 -8n^2+20n-13 a prime number??

1. sheg

factorize it

2. King

how watever i get is not a prime number

3. King

why?

4. King

oh

5. King

but then ii have to plug in millions of values

6. sheg

what u want to calculate

7. sheg

(n^3 -8n^2+20n-13) a prime number

8. sheg

or n is a prime number

9. King

for n i will have to put millions of values to find how may n positive integers satisfy n^3 -8n^2+20n-13 to be a prime number

10. sheg

ok

11. King

so,what to do??

12. King

anything i can do to narrow down the possobilities

13. King

14. sheg

ok see for 2 it is prime number

15. sheg

wait i took wrong concept

16. sheg

$(x-1) \times [(x-7)x + 13]$

17. sheg

where x is n

18. King

ok

19. sheg

now see the first term is (x-1). and other than 2 no other even number is a prime number right

20. sheg

i got the answer

21. King

no n does not have to be a prime number n^3 -8n^2+20n-13 has to be a prime number

22. sheg

yeah i know (x−1)×[(x−7)x+13] it has to be prime

23. King

yup so x can be anything greater or equal to 2

24. sheg

first term is (x-1) and two is the only even prime number.

25. sheg

but if u will subtract 1 from any other prime number the resultant will be divisible by 2

26. sheg

getting my point or not

27. King

x can be 4

28. sheg

yeah u r right

29. sheg

it means that for any odd integer other than 3 u will not get a prime number

30. King

yeah

31. FoolForMath

Superb sheggy!

32. sheg

also the number cannot be graeter than 7

33. King

oh yeah

34. sheg

thanks fool bhai

35. sheg

so u are having a limited space to work out that is from 1 to 7

36. King

yes sheg u got it so answer is n=2,3,4

37. King

no actually 2 to 7

38. sheg

hahahaa right 2 to 7

39. sheg

but for 7 it will be 0

40. King

wait why cant it be greater than 7?

41. sheg

try any number u will get the answer

42. sheg

odd numbers cannot be included ok thats true

43. sheg

as i had told u any odd number subtracted by one will result in even number so it will be divisible by 2.........do u accept it or not

44. King

is 323 a prime number?

45. King

yeah i acept

46. King

its not div by 17

47. sheg

323 is divisible by 17

48. sheg

so 323 is not a prime number

49. King

4387 ?

50. sheg

what u have put x = ??

51. King

n=20

52. King

1443?

53. King

gtg shall come bak in 15 min

54. sheg

for n = 20 it should be equal to 5187

55. King

oh yeah 1443?

56. King

no

57. sheg

20^3 - 8*20^2 + 20*20 -13 =8000 - 3200 + 400 -13 = 8400 - 3213 = 5187

58. King

gtg cum bak in 15 mins

59. sheg

dear i had told u for no value greater than 7 it would fit

60. sheg

and both 1443 and 5187 is divisible by 3

61. King

i am bak so what to do now?

62. sheg

for no value greater than 7 that too even number it will not be a prime number

63. sheg

http://www.wolframalpha.com/input/?i=x^3-8x^2%2B20x-13+where+x+%3D+20 visit this website and plug in different value of x u will get the answer

64. sheg

king u there