Math Is Fun Forum

Stangerzv

Member

Registered: 2012-01-30

Posts: 266

New Prime of the form "2 to the power-n"(Powerful Computing Required)

Consider this equation

Where P1, P2 are  Primes numbers greater than 2, n is an integer and Ps is the resulting Prime

My computer Intel core I5 seems won't be able to calculate the prime beyond n>50 when P1 & P2 not even larger than 20.

Taking log on one prime yields:

2^nlogP1, when n=20, and P>10, the prime calculated could be at least 1 million digits.

Some primes are governed by this generalize equation and can be read here www.oeis.org.

Last edited by Stangerzv (2013-06-23 16:53:16)

Stangerzv

Member

Registered: 2012-01-30

Posts: 266

Re: New Prime of the form "2 to the power-n"(Powerful Computing Required)

Examples:

1) Prime http://oeis.org/A121824

2)

Ps=29, {1 106797 700023 024077 725094 307737 472968 581258 525130 036534 958183
195262 352487 003994 998424 001716 919039 694617 585799 997538 773692 828512
364527 389432 832278 502186 775641 690620 955004 441454 802124 251331 895165
393028 954365 090623 874561}....My computer failed to calculate further.

3)

Ps=107182721..My Computer failed on calculating for n>12

4)

Ps=89, 14321, .. My Computer failed on calculating for n>12

4)

Ps=149, 41801, 3487882001, 24330595937854957601 .. My Computer failed on calculating for n>12

5)

Ps=37, 16692759230113....My computer failed on calculating for n>15.

Last edited by Stangerzv (2013-06-23 14:53:09)