A379020 Numbers k such that 2^k - 25 is prime.

5, 7, 9, 13, 33, 37, 57, 63, 93, 127, 129, 165, 189, 369, 717, 3079, 3087, 3925, 6709, 7633, 18001, 21961, 55557, 60415, 63589, 69463, 75949, 98265, 212295, 416773, 647545, 824325, 1538959, 2020893, 2421175

Offset: 1

Author

Boyan Hu, Dec 13 2024

Keywords

• nonn
• more

Comments

Except for a(1), all terms are congruent to 1 or 3 mod 6.

a(36) > 3400000. - Boyan Hu, Jun 16 2025

Examples

			7 is in the sequence because 2^7-25=103 is prime.
8 is not in the sequence because 2^8-25=231=3*7*11 is not prime.
		

Links

• Henri Lifchitz and Renaud Lifchitz (Editors), Search for 2^n-25, PRP Top Records.
• Boyan Hu, 2^n-25 PRP searching progress

Crossrefs

Sequences of numbers k such that 2^k - d is prime: A000043 (d=1), A050414 (d=3), A059608 (d=5), A059609 (d=7), A059610 (d=9), A096817 (d=11), A096818 (d=13), A059612 (d=15), A059611 (d=17), A096819 (d=19), A096820 (d=21), A057220 (d=23), A356826 (d=29).

Except for a(1), subsequence of A047241.

Programs

Mathematica

Do[ If[ PrimeQ[ 2^n - 25 ], Print[ n ] ], { n, 1, 15000} ]

PARI

is(n)=ispseudoprime(2^n-25)

Extensions

a(1)=5 inserted by Max Alekseyev, May 28 2025