Grid of Primes
 

This shoudn't be too hard.

Construct a 5x5 grid with the center box closed off (like a crossword),
filled with 24 odd digits (one per grid box), such that each number
formed from the digits of an entry (in either order) is prime. Here an
entry is either a 5-row or 5-column or one of the four 2-boxes connected
to the middle closed box. No prime may be repeated.

To make this interesting, find a solution which minimizes or maximizes
either the sum of the digits in the boxes or the sum of the primes formed.

This is probably suboptimal for a minimal solution:
[spoiler]
10003 | 00013, 00007, 0000000137 (north)
00070 | 00017, 00053, 0000001753 (south)
01X00 | 00015, 00071, 0000001571 (west)
05030 | 00031, 00037, 0000001373 (east)
70001 | 000000000000000011135737 (all)
[/spoiler]
sum: 11140815

Not what I intended, probably due to my description.
I intended a 5x5 array of odd digits (from {1,3,5,7,9}),
(excluding the center element), like:

17339
33797
17x31
95759
19937

but with all four full rows and their reversals (like 17339 and 93371)
and all four full columns and their reversals (like 13191 and 19131)
and all eight two-digit middle-half rows (like 37 and 73 and 31 and 13)
prime (which is NOT true in this example).

What direction do we read the short primes in?

[QUOTE=CRGreathouse;204478]What direction do we read the short primes in?[/QUOTE]Say way you read this forum.

[quote=CRGreathouse;204478]What direction do we read the short primes in?[/quote]First one way, then the other. Has to be prime both ways.

Or, maybe you mean: north, south, east, and west from center (not NE, NW, SE or SW).

[quote=cheesehead;204532]First one way, then the other. Has to be prime both ways.

Or, maybe you mean: north, south, east, and west from center (not NE, NW, SE or SW).[/quote]

This still doesn't make sense to me. Can you be more specific? Let's use your box as an example. Here it is repeated:

17339
33797
17x31
95759
19937

So, are the 4 small primes as follows?:
1733
3979
9591
5973

That would go top-left, top-right, bottom-right, bottom left for each 4-box, or in directional terms for each box, it would be the NW most digit, the NE most digit, then SE, and finally SW.

In other words, reading it around-the-horn like a circle.

If so, are the backwards "primes" simply the reverse of the above?

I guess it would be easiest if you just specified the small "primes" in your box. Then we can figure out the direction of them.


Gary

[quote=gd_barnes;204536]This still doesn't make sense to me. Can you be more specific?[/quote]

I guess he wants

[code]abcde
fghij
jkXlm
nopqr
stuvw[/code]with all of these prime:

abcde, edcba, fghij, jihgf, nopqr, rqpon, stuvw, wvuts
afjns, snjfa, bgkot, tokgb, dilqv, vqlid, ejmrw, wrmje
ch, hc, jk, kj, lm, ml, pu, up

... which is, of course, impossible without repetition, since there are only 5 reversible two-digit primes (plus their respective reverse ones). :smile:

[QUOTE=ckdo;204562]... which is, of course, impossible without repetition, since there are only 5 reversible two-digit primes (plus their respective reverse ones). :smile:[/QUOTE]

Thus my question.

[QUOTE=ckdo;204562]... which is, of course, impossible without repetition, since there are only 5 reversible two-digit primes (plus their respective reverse ones). :smile:[/QUOTE]

huh? you only need 4. so where's the impossibility?