WON TOPIC 148

World!Of Numbers		WON plate 148 \|
[ May 4, 2003 ] A simple search puzzle... with hard to find solutions Concatenate two neighbouring primes (none, one or maximum two primes skipped) so that you end up with a square !

GIVE ME TWO PRIMES FOR A SQUARE PLEASE

SKIP PRIMES CONCATENATED
PRIMESET ROOT AUTHOR

0
two successive
primes 1 411828016678198512725064549221
411828016678198512725064549241
641738277398347583345401533579 = p
= q = pq^(1/2) Giovanni
Resta

2 p q pq^(1/2) ?

3 p q pq^(1/2) ?

4 p q pq^(1/2) ?

5 p q pq^(1/2) ?

RND p q pq^(1/2) ?

1
one prime
skipped 1 2 5 5 pdg

2 623387 623401 789549 pdg

3 p > 100,000,000 q pq^(1/2) pdg

4 p q pq^(1/2) ?

5 p q pq^(1/2) ?

RND p q pq^(1/2) ?

2
two primes
skipped 1 47 61 69 pdg

2 p > 100,000,000 q pq^(1/2) pdg

3 p q pq^(1/2) ?

4 p q pq^(1/2) ?

5 p q pq^(1/2) ?

RND p q pq^(1/2) ?

[May 7, 2003 ]
Jean Claude Rosa considered the case p > q
and found the following nice solutions :

1
one prime
skipped 1 2137 2129 4623 jcr

2 809821 809801 899901 jcr

3 p q pq^(1/2) ?

RND p q pq^(1/2) ?

[May 17, 2003 ]
Giovanni Resta (email) found the smallest solution
for the case with no gaps : p_(k)p_(k+1) = x^2

411828016678198512725064549221 || 411828016678198512725064549241 =
641738277398347583345401533579²

For the reverse case whereby p > q or p_(k)p_(k-1) = x^2
he found the following three solutions :

607286296388662783 || 607286296388662769 =
779285760416974887²

999800009999800021 || 999800009999800001 =
999899999999900001²

126896403745276627317710453 || 126896403745276627317710401 =
356225214920668729628553951²

A000148

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