$51456$, $541456$, $331259$ and $92020$.

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Ec primes are primes formed by concatenation in base ten of two consecutive Mersenne numbers, $40952047$, for example.

Some exponents leading to an ec prime are: $51456$, $541456$, $331259$ and $92020$.

It is easy to see that $331259=541456+13-210210$ and $92020=331259-239239$.

Now $92020\equiv -25\pmod {449}$

$541456 +13\equiv -25\pmod {449\cdot 201}$

$210210\equiv 78\equiv -239239 \pmod {449}$

$51456$ is a multiple of $201$.

Is it possible that all this has some explanation?