Problems & Puzzles: Puzzles

Puzzle 132.  Pascal Primes

For sure you know the Pascal triangle:

 Row Pascal triangle 1 1 2 1 1 3 1 2 1 4 1 3 3 1 5 1 4 6 4 1 6 1 5 10 10 5 1 7 1 6 15 20 15 6 1 8 1 7 21 35 35 21 7 1 9 1 8 28 56 70 56 28 8 1 etc etc

Concatenating the numbers in each row, the following rows are primes: 2, 9, 30, ?

Questions:

a) Find the fourth prime-row.
b) The 9th row reversed is prime also. What other rows reversed are primes?

Solution

Paul Jobling sent the following (10/4/01) for our question b)

"You ask about reversed rows being prime.

row 2 = 11
row 7 = 1651025161
row 9 = 18826507658281
row 10 = 196348621621486391
row 11 = 1015402101225201202154011
row 33=12369406940695367310229160965856330038150100884/
082042215460844209210482975220063737430065341740272275/
650930801060272275650065341740063737430482975220844209/
210422154600884082003815016585633291609673102069530694694231

Titanix was used to prove these prime".

(Note: this doesn't mean that these primes are reversible)

***

J. K. Andersen wrote (Jun 2003):

PrimeForm/GW found only the already known primes in the first 696 rows and reversed rows. The search stopped before row 697 which has 104568 digits if anyone feels lucky.

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