Number Choosing Contest.

1061, a pure and innocent number.

PASSES 1 4 U V
FAILS 2 3 5 R

-4 : a negative integer

(3756801695685 · 2^666669 - 1) :largest known prime

19997 : largest prime less than 20,000

77777: not a prime

4: a positive integer

-4: Breaks
2 3 4 R U

LARGEST KNOWN PRIME:
Rule 1: Uncertain. Computational resources currently limited.
Rule 2: Breaks.
Rule 3: Uncertain. Computational resources currently limited.
Rule 4: Passes.
Rule 5: Breaks.
Passes format rules.

19997:
Rule 1: Breaks.
Rule 2: Breaks.
Rule 3: Close! But it breaks.
Rule 4: Passes.
Rule 5: Breaks.
Breaks R U

77777:
Rule 1: Breaks.
Rule 2: Breaks.
Rule 3: Breaks.
Rule 4: Passes.
Rule 5: Breaks.
Breaks R U

4:
Breaks 2 3 R U

123454321: a palindrome

1998001: the hypotenuse of a (very large) pythagorean triple

root(2): an irrational algebraic number

sum(from n = 1 to infinity) 1/n^2: a transcendent number (which happens to be equal to (pi^2)/6, which is SO COOL)

85: a number with both a five and an eight

123454321: Breaks
3 R U (Closest one so far for the number rules!!)

1998001: Breaks
1 2 3 5 R U

sqrt2:
Rule 1: Breaks.
Rule 2: Breaks.
Rule 3: Breaks.
Rule 4: Breaks.
Rule 5: Breaks.
Passes format rules.

Riemann Zeta 2:
Rule 1: Breaks.
Rule 2: Breaks.
Rule 3: Breaks.
Rule 4: Breaks.
Rule 5: Breaks.
Passes format rules.

85: Breaks
2 5 R U


Breaks 1 2 3 5 R U

(whether my post count is odd && whether it is raining when you answer this) || (whether the minute time I post this is even ^^ !whether the person who posts after me is male)

the first four positive integers that can be represented as the sum of two nonzero cubes.

Both 0 and 1 have already been submitted so either way you already know.

2: Breaks 1 2 3 5
9: Breaks 1 2 U
16: Breaks 2 3 U
28: Breaks 1 2 3 5 U

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Spoiler

Eight.

8: Breaks 1 2 3 5.