Wikipedia:Reference desk/Archives/Mathematics/2017 January 25

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January 25

What is the highest number with all permutations of its digits being prime?

Something like 991. 199 and 919 are still prime. Sagittarian Milky Way (talk) 02:26, 25 January 2017 (UTC)

See Permutable prime. There are probably infinitely many repunit primes, the special case where all digits are 1's so there is no other permutation. 991 is probably the largest non-repunit permutable prime. PrimeHunter (talk) 02:41, 25 January 2017 (UTC)

Other bases have permutable primes with more permutations. I quick calculation found the 8-digit base 494 number with a 445 followed by seven 297's. This has 8 permutations, all prime. In decimal it's 3199161737666234740307. PrimeHunter (talk) 03:25, 25 January 2017 (UTC)

as of this moment, this page is the only use of "base 494 number" found in google search Naraht (talk) 16:10, 25 January 2017 (UTC)

Lol. Imagine a culture with base-5093. "The number atlatl monkey monkey monkey monkey monkey monkey monkey is the first cat-digit permutable prime. It is conjectured that there are no house-digit permutable primes below base-spark plug."... Sagittarian Milky Way (talk) 19:06, 25 January 2017 (UTC)

I'm not sure this is even imaginable. How would they learn to add and multiply, without breaking down the numbers into sub-bases like the Sumerians did with their base-60? Still, digits to base-360 have indeed been invented (link) by an architect (Michael de Vlieger), and with the principles described you could conceivably go on until 653, where you run out of chemical elements to give the glyphs for the primes. Double sharp (talk) 04:47, 28 January 2017 (UTC)

Rounding choice

Removed duplicate question. See it on the Science Desk, here. --76.71.6.254 (talk) 01:11, 26 January 2017 (UTC)

Algorithm

I have [(q)(e)]+[(j)(1-q)]=[(q)(g)]+[(m)(1-q)]. What algorithm solves for q? I'm having trouble with this algebra... Schyler (exquirere bonum ipsum) 19:11, 25 January 2017 (UTC)

Isn't this just a linear equation in q? If not, maybe you could define notation and explain the context. Loraof (talk) 20:40, 25 January 2017 (UTC)

I want to find if a game has a Mixed Strategy Nash Equilibrium quickly in Excel. q is the probability of playing strategy a, 1-q is the probability of playing strategy b. e, j, g, and m are the payoffs of strategies c and d. It makes sense that this could "just" be a linear equation, but I want to be able to do the algebra by hand, but I'm not getting it. Schyler (exquirere bonum ipsum) 22:19, 25 January 2017 (UTC)

Combine like terms to get $q(e-j-g+m)=-j+m$, and divide through by the coefficient of q to solve for q. Loraof (talk) 23:04, 25 January 2017 (UTC)

I'm thinking if that didn't come to him on its own, the "coefficient of q" might be confusing. So I should say explicitly that to me the above means $q={\frac {m-j}{m-j+e-g}}$. Wnt (talk) 00:59, 26 January 2017 (UTC)

Ohh, the undistributive property ;) Thanks you guys! Schyler (exquirere bonum ipsum) 03:58, 26 January 2017 (UTC)

The general rules for solving any linear equations are:

1. Clear fractions by multiplying each term by the common denominator (not needed here)

2. Multiply out brackets

3. Collect terms (putting all the terms containing the required letter on one side and all other terms on the other side

4. Factorise (or factorize in American math)

5. Divide (to get the required letter on its own

This should help to solve similar problems. Dbfirs 08:57, 26 January 2017 (UTC)