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fivefive Batch , stdin/stdout

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fivefive.html

Five, Five Everywhere

Problem Statement

Print a sequence a1, a2, ..., aN whose length is N that satisfies the following conditions:

  • ai (1 ≤ i ≤ N) is a prime number at most 55 555.
  • The values of a1, a2, ..., aN are all different.
  • In every choice of five different integers from a1, a2, ..., aN, the sum of those integers is a composite number.

If there are multiple such sequences, printing any of them is accepted.

Notes

An integer N not less than 2 is called a prime number if it cannot be divided evenly by any integers except 1 and N, and called a composite number otherwise.

Limits

  • 5 ≤ N ≤ 55

Subtask 1 (20%): 5 ≤ N ≤ 10

Subtask 2 (20%): 5 ≤ N ≤ 20

Subtask 3 (60%): No additional constraints

Subtask 4 (0%): Sample

Input

Input is given from Standard Input in the following format:

N

Output

Print N numbers a1, a2, a3, ..., aN in a line, with spaces in between.

Sample Input 1

5

Sample Output 1

3 5 7 11 31

Let us see if this output actually satisfies the conditions.
First, 3, 5, 7, 11 and 31 are all different, and all of them are prime numbers.
The only way to choose five among them is to choose all of them, whose sum is a1+a2+a3+a4+a5=57, which is a composite number.
There are also other possible outputs, such as 2 3 5 7 13, 11 13 17 19 31 and 7 11 5 31 3.

Sample Input 2

6

Sample Output 2

2 3 5 7 11 13
  • 2, 3, 5, 7, 11, 13 are all different prime numbers.
  • 2+3+5+7+11=28 is a composite number.
  • 2+3+5+7+13=30 is a composite number.
  • 2+3+5+11+13=34 is a composite number.
  • 2+3+7+11+13=36 is a composite number.
  • 2+5+7+11+13=38 is a composite number.
  • 3+5+7+11+13=39 is a composite number.

Thus, the sequence 2 3 5 7 11 13 satisfies the conditions.

Sample Input 3

8

Sample Output 3

2 5 7 13 19 37 67 79

Tags

AtCoder, Number Theory, Math

Subtasks and Limits

Subtask Score #TC Time Memory Scoring
12041s256MBMinimum
22051s256MBMinimum
36061s256MBMinimum
4031s256MBMinimum

Judge Compile Command

g++-8 ans.cpp -o fivefive -Wall -Wshadow -static -O2 -lm -m64 -s -w -std=gnu++17 -fmax-errors=512

Accepted Submissions

subIDUserTimeMax Time

Past Submissions

subIDUserTimeScore
mrJudge 09.05.20
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