71828...37113 (357-digits)

This number is a prime.

                                                                     7182818
2845904523 5360287471 3526624977 5724709369 9959574966 9676277240 7663035354
7594571382 1785251664 2742746639 1932003059 9218174135 9662904357 2900334295
2605956307 3813232862 7943490763 2338298807 5319525101 9011573834 1879307021
5408914993 4884167509 2447614606 6808226480 0168477411 8537423454 4243710753
9077744992 0695517027 6183860626 1331384583 0007520449 3382656029 7606737113

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The first 357 digits after the decimal point in e form a prime, as do the first 1, 2, 49, 114, 126 and 295. Note that the first 1090 form a titanic probable prime.

UPDATE: In December 2000, after 29+ hours of computer time, Andrey Kulsha proved via Titanix that the first 1090 digits is indeed prime. [Broadhurst , Kulsha]