Sum of Primes
All submissions for this problem are available.$f$ is a function such that $f(x)$ equals the number of ways in which $x$ can be expressed as sum of two prime numbers. For example $f(10) = 2$, as 10 can be expressed as sum of two primes in two ways: $ 3 + 7 = 5 + 5 = 10$. More formally, $f(x)$ is the number of pairs $(a, b)$ such that $0\le a \le b < x$ and $a$ and $b$ are prime and $a + b = x$. Given an integer $N$, find the number of pairs $(a, b)$ such that $0 \le a \le b < N$ and $f(a) + f(b) = f(N)$. ###Input: - First line will contain $T$, number of testcases. Then the testcases follow. - Each testcase contains of a single line of input, a integer $N$. ###Output: For each testcase, output in a single line, the required answer. ###Constraints - $1 \leq T \leq 5$ - $0 \leq N \leq 10^6$ ###Sample Input: 3 1 5 10 ###Sample Output: 1 4 21 ###Explanation: - **Case 1:** $f(0) = f(1) = 0$. So the only way to express $f(1)$ is as $f(0) + f(0)$. - **Case 2:** $f(0) = f(1) = f(2) = f(3) = 0$, and $f(4) = f(5) = 1$. So $f(5)$ can be expressed as $f(0) + f(4)$, $f(1) + f(4)$, $f(2) + f(4)$ and $f(3) + f(4)$.
|Tags||avijit_agarwal, cole2018, fft, medium, sieve|
|Time Limit:||1 sec|
|Source Limit:||50000 Bytes|
|Languages:||C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, kotlin, PERL6, TEXT, SCM chicken, CLOJ, COB, FS|
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