Problems & Puzzles: Puzzles

Puzzle 881. 123456789 and prime numbers.

Very recently I saw the following curio somewhere out there:

123456789 = ((86+27)^591)/3^4

This expression:

a) uses the same 9 digits in both parts of the equality, only once in each side.
b) uses all the four arithmetical basic operators and the power operator, plus parentheses.
c) uses four (4) primes: 2, 3, 5, & 7 and three composites 4, 86 & 91.

Here we ask for other similar arithmetical expressions of 123456789 but using more than four prime numbers. Hint: the maximal quantity of primes that you may use is six (6)

Q1. Send your best expression for 123456789 (maximal quantity of primes)
Q2. Redo Q1 for 987654321


Contributions came from Emmanuel Vantieghem,


Emmanuel wrote:

Q2 : 987654321=(8*(94+6)^5+1)/(3*27), two primes.


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