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Problems & Puzzles:
Puzzles
Puzzle 1266 Primes
type
3+141592653589793238462643383279...
& more
In one of the
Curios form the alway intersting site
Prime Curios!
of my friend G. L. Honaker, Jr., we can read:
3+141592653589793238462643383279502884197169399375105820974944592307816406286208998628
(84 digits) is a prime
number.
Note that the decimal point is replaced with a plus
sign in the expansion of π. [Honaker].
(Verified by CR using
ECM
&
https://www.angio.net/pi/ )
Q1. Find a larger
prime of thase type.In
another
curio we can read:
7753757725325377
is a 16-digit prime-digits
prime; occurs at position 31174962
of π. [Honaker].
(Verified by CR using
ECM
&
https://www.angio.net/pi/ )
Q2. Find a larger
prime of these type.
Finnaly, in another
Curio, we can read:
314 is the
smallest pisemiprime
(i.e., a semiprime) formed
by the initial digits of the decimal expansion of π.
The sequence begins 314,
314159265358, 314159265358979323,
3141592653589793238462643383279502, ... . [Najafi]
314 = 2 x 157 (Non-Brilliant pi-semiprime)
314159265358 = 2 × 157079632 (Non-Brilliant
pi-semiprime)
314159265358979323 = 317213509
x 990371647 (Brilliant semiprime because it
has the prime factors with the same quantity of
digits)
3141592653589793238462643383279502 =
2×1570796326794896619231321691639751 (Non-Brilliante
pi-semiprime)
(Factorizations verified by CR using
ECM)
Q3. Continue this
sequence.
Q4. Find a larger Briliiant
pi-semiprime
* Brilliant numbers,
as defined by Peter Wallrodt
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