A few candiates in the range 18*10^5-19*10^5

enzocreti · 2019-03-25, 07:58

pg(k) numbers are so defined:
they are the concatenation in base 10 of two consecutive Mersenne prime so for example the first few are: 10,31,73,157,3115,6331,12763,255127...
some of them are obviously prime.
They are of the form (2^k-1)*10^d+2^(k-1)-1, with d the number of dec digits of 2^(k-1)-1
I realized that the all ec(43s)'s which are probable primes have the form ec(41j+m) with j,m some positive integers. The known examples are ec(215) (prime), ec(69660) prp, ec(92020) prp, ec(541456) prp.
Now I sieved with Pari the possible candidates for such a prime in the range 18-19*10^5.
Here the vector k=[1805699, 1810515, 1812579, 1814471, 1818556, 1821523, 1821566, 1828446, 1828618, 1835498, 1839196, 1839712, 1846076, 1848011, 1848527, 1853816, 1858116, 1861943, 1862631, 1870758, 1874972, 1881336, 1881508, 1884862, 1884991, 1889850, 1891914, 1892086, 1895139, 1895440]

Would somebody test at random at least one of this numbers if any is ever probable prime?

2019-03-25, 07:58	#1
enzocreti Mar 2018 2×5×53 Posts	*A few candiates in the range 1810^5-1910^5* pg(k) numbers are so defined: they are the concatenation in base 10 of two consecutive Mersenne prime so for example the first few are: 10,31,73,157,3115,6331,12763,255127... some of them are obviously prime. They are of the form (2^k-1)10^d+2^(k-1)-1, with d the number of dec digits of 2^(k-1)-1 I realized that the all ec(43s)'s which are probable primes have the form ec(41j+m) with j,m some positive integers. The known examples are ec(215) (prime), ec(69660) prp, ec(92020) prp, ec(541456) prp. Now I sieved with Pari the possible candidates for such a prime in the range 18-1910^5. Here the vector k=[1805699, 1810515, 1812579, 1814471, 1818556, 1821523, 1821566, 1828446, 1828618, 1835498, 1839196, 1839712, 1846076, 1848011, 1848527, 1853816, 1858116, 1861943, 1862631, 1870758, 1874972, 1881336, 1881508, 1884862, 1884991, 1889850, 1891914, 1892086, 1895139, 1895440] Would somebody test at random at least one of this numbers if any is ever probable prime?

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