Number Choosing Contest.

13


17


19


-1


12

6

7

9

11

6:
Breaks rules 3, 4, and 5

7:
Breaks rules 1 and 4

9:
Breaks rules 2, 3, and 4

11:
Breaks rules 2, 4, and 5

13


17


19


-1


12

13:
Breaks rules 4 and 5

17:
Breaks rules 1, 2, 4, and 5

19:
Breaks rules 2 and 4

-1:
Breaks prerequisite ε

12:
Breaks rules 2, 3, 4, and 5

Also, I made two mistakes in my earlier post. I've fixed them now.

I think I know the first rule.

No clue about the second.

10

14

15

16

18

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20


21


22


23


24

25

2003

9157

73

97

70

113

Largest known prime

I think I know the first rule.

No clue about the second.

10

14

15

16

18

10:
Breaks 2, 3, 4, and 5

14:
Breaks 3, 4 and 5

15:
Breaks 3 and 5 (First to pass rule 4!)

16:
Breaks 2, 3, and 4

18:
Breaks 2, 3, 4, and 5


False. The integers are infinite.

-5:
Breaks prerequisite ε

20


21


22


23


24

20:
Breaks rules 3, 4, and 5

21:
Breaks rules 3, 4, and 5

22:
Breaks rules 3, 4, and 5

23:
Breaks rules 2, 4, and 5

24:
Breaks rules 2, 3, 4, and 5

25

2003

9157

25:
Breaks rules 2, 3, 4, and 5

2003:
Breaks rules 4 and 5

9157:
Breaks rules 1, 4, and 5.

Still no clue about even rule 2.

26

27

28

29

30

That last batch would appear to contain counterexamples to my ideas for rules 2 and 3. Hmph.

31

32

225

811

50625

whoops, 9157 does NOT break rule 3.
Sorry.

Still no clue about even rule 2.

26

27

28

29

30

26:
Breaks rules 2, 3, and 4

27:
Breaks rules 1, 3, 4, and 5

28:
Breaks rules 3 and 4

29:
Breaks rules 4 and 5

30:
Breaks rules 2, 3, 4, and 5

That last batch would appear to contain counterexamples to my ideas for rules 2 and 3. Hmph.

31

32

225

811

50625

31:
Breaks rules 2 and 5

32:
Breaks rules 2, 3, 4, and 5

225:
Breaks rules 3, 4, and 5

811:
Breaks rules 4 and 5

50625:
Breaks rules 3, 4, and 5

How does 631 fare?

How does 631 fare?

Breaks only rule 4!

Right, now I need to figure out what rule 4 is...

39

63

95

8191

654321

8658

Does 18 really not break rule 2?

In either case I think I've got rules 2 and 3 and 4. Good times. Thank Mathematica for generating my number candidates.


223

239

463

911

1231

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SpoilerShow

Mathematica is great.

1583

2143

2239

2351

2591

Kaynato, if I understand what you think rule 4 is correctly, you're going to have to count for quite a while to get something that is also rule 5 compliant.

Up to 33391, to be exact.

You are not necessarily correct.

In either case, my suspect rule 4 is probably wrong. It feels too simple.

The following numbers should follow rules 1, 2, 3, and 5.

These should confirm whether I am correct about rule 4.

631

2269

5419

9241

33391 (follows all rules if I am correct)

Edit: Oh, as it turns out I miswrote my rule 4 :v

I'll still submit these.

I agree with you that it seems a bit simple in comparison, and that the numbers you've submitted would then follow the rules that you say they would. I got to 33391 with a calculator rather than Mathematica, but it still stands that it may pass everything...

The first four numbers in the previous area then should break rule 4.

For extra safety, the following numbers pass rules 1, 2, 3, and 5

42841

114661

260191 (Also rule 4)

351919 (Also rule 4)

1653919 (Also rule 4)

Does 18 really not break rule 2?

Oh, right, yes it does. Let me change that.