For how many positive integers n are there exactly ⌊n/2⌋ or ⌈n/2⌉ primes less than or equal to n ? ⌊⌋ = the largest integer less than or equal to x.⌈⌉ = the smallest integer greater than or equal to x.
for 1, we have 0 prime number...
for 2, we have 0
for 3, we have 1
4 we have 2...
for every odd number n+1/2 and n-1/2 are least integer greater than equal to and greatest integer less than equal to value of n/2
after a certain number, the number of prime numbers start decreasing,
for 5 we have 2
6 we have 3
7 we have 3
8 we have 4
9 we have 4
10 we have 4...
11 we have 4,,,
12 we have 5//
13 we have 5
so we have 1,3,4,5,6,7,8,9 as the numbers which satisfy as the value of n... 8 such numbers..
a point is picked... now any point when joined with this making a chord having central angle greater than 60 degree, would be more than 1cm away...120 degrees in total...(both clockwise and anticlockwise)
For how many positive integers n are there exactly ⌊n/2⌋ or ⌈n/2⌉ primes less than or equal to n ? ⌊⌋ = the largest integer less than or equal to x.⌈⌉ = the smallest integer greater than or equal to x.
n = 1 to 9 and n=11,13 attributed to the fact that prime numbers occur at higher frequency for the first few natural numbers and then the gap offsets any further possibility.
for 1, we have 0 prime number...for 2, we have 0for 3, we have 1 4 we have 2...for every odd number n+1/2 and n-1/2 are least integer greater than equal to and greatest integer less than equal to value of n/2after a certain number, the number of prime numbers start decreasing, for 5 we have 26 we have 37 we have 38 we have 49 we have 410 we have 4...11 we have 4,,,12 we have 5//13 we have 5so we have 1,3,4,5,6,7,8,9 as the numbers which satisfy as the value of n... 8 such numbers..
I think you have missed the word "less than or equal to n"
for n=2, primes
So, n takes all values from 1 to 9,there is a break at 10, which has 4 and 12, which has 5. However n=11 and 13 satisfy with 5 and 6 primes respectively.
n = 1 to 9 and n=11,13 attributed to the fact that prime numbers occur at higher frequency for the first few natural numbers and then the gap offsets any further possibility.Hence total 11 such values of n are there.Team BV -Vineet
for n = 2 , we have greatest and smallest integer as 1, but no prime number less than 2(1 is not a prime number).... for 11 we have 5 and 6... no. of prime numbers less than 11 are 2,3,5,7/.. and so for 13...
for n = 2 , we have greatest and smallest integer as 1, but no prime number less than 2(1 is not a prime number).... for 11 we have 5 and 6... no. of prime numbers less than 11 are 2,3,5,7/.. and so for 13...
@albiesriramIs it (c) 6 ?For first two no's 12 , difference is 1.for first four no's 1234, diff is 2,for first 6 no's 123456, diff is 3..for 100 no's diff is 5050/11 = 6.
