Problems & Puzzles: Puzzles

Puzzle 957. Largest prime with pandigital ordered expressions Carlos Rivera asks this: Find large primes as arithmetic expressions using just one of each of the following integers in rigorous order: a)       1,2,3,4,5,6,7,8,9 b)      1,2,3,4,5,6,7,8,9,0 c)       9,8,7,6,5,4,3,2,1 d)      9,8,7,6,5,4,3,2,1,0 and using only the following five arithmetical operators +, -, *, /, ^ and parentheses "(" and ")" as auxiliary symbols. Examples: a)       1+2^3+4^5+6^(7+8+9) = 4738381338321617929 (19 digits, prime!) b)      1+2^3+4^5+6^7*8^90 = 5310771084122086847626078987778794811033679696258 78641622214217512372958967973873189897 (87 digits, prime!) c)       9^87-6^(5-4)+3^2+1 = 10449567633177831596610387890345070198960878107 3244439950619431748912396904023371773 (84 digits, prime!) d)      9^8*7^6*5^4*3-2+10 = 9495756897991883 (16 digits, prime!) Q. Send your three largest primes for each type of expression.

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Contributions came from Paul Cleary

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Paul wrote on June 20, 2019

Here are my largest 3 primes for each type.

Type a.

1+2*3^4^5-67-8-9, 489 digits.

1*2+3^4^5+67+8+9, 489 digits.

-1*2+3^4^5+6-7+89, 489 digits.

Type b

-123^4-5+6+7^890, 753 digits.

-12^3*4^5-6+7^890, 753 digits.

1+2+3^4*5+6+7^890, 753 digits.

Type c.

9+8^765+43*2*1, 691 digits.

-9*8+7^654+3+2-1, 553 digits.

-9+8^7*6^5^4-3+2-1, 493 digits.

Type d.

9+8^765-4+3^2*10, 691 digits.

-9*8+7^654-3*2+10, 553 digits

-9^8+76^5+4*3^2^10, 490 digits

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