Problems & Puzzles: Puzzles

Puzzle 1208 Prime(6n)-6Prime(n) Sebastián Martín Ruiz sent the following puzzle: Prime(6n)-6Prime(n) is pirme for n=2 to 13 19,31,47,47,73,79,109,113,107,131,137, 151, Q) Find a larger set of consecutive primes for another k value in Prime(kn)-kPrime(n)

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From Feb 17-23, 2025, contributions came from Michael Branicky, Oscar Volpatti

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Michael wrote:

I searched values of k=1..10^7 over primes < 10^10.

The largest set of consecutive primes matched

Sebastián's 12 when k = 6 and n = 2..13.

The second largest was 8 for k = 2 and n=16907875..16907882. Primes are:

24841501, 24841501, 24841501, 24841529, 24841543, 24841499, 24841499, 24841543

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Oscar wrote:

Dear Carlos,

I found a set of 14 consecutive primes for parameter k=30030 and for index n from 2648412 to 2648425:

i  n  Prime(n)  Prime(k*n)  Prime(k*n)-k*Prime(n)

01  2648412  43772167  2176724762063  862246587053

02  2648413  43772189  2176725613273  862246777603

03  2648414  43772227  2176726469077  862246492267

04  2648415  43772231  2176727320687  862247223757

05  2648416  43772269  2176728176123  862246938053

06  2648417  43772273  2176729033159  862247674969

07  2648418  43772293  2176729885487  862247926697

08  2648419  43772303  2176730737679  862248478589

09  2648420  43772347  2176731586349  862248005939

10  2648421  43772357  2176732441603  862248560893

11  2648422  43772383  2176733293601  862248632111

12  2648423  43772389  2176734149033  862249307363

13  2648424  43772401  2176735003489  862249801459

14  2648425  43772413  2176735856987  862250294597

 

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