A087714
Primes p = prime(i) such that p(i)# - p(i+1) and p(i)# + p(i+1) are both primes, where p# = A002110.
Original entry on oeis.org
2*3*5-7 = 23 is prime, 2*3*5+7 = 37 is prime.
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isok(p) = {if (isprime(p), my(pp = prod(k=1, primepi(p), prime(k)), q = nextprime(p+1)); isprime(pp-q) && isprime(pp+q););} \\ Michel Marcus, Sep 20 2019
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my(pr=1); forprime(p=1, , pr=pr*p; if(ispseudoprime(pr-nextprime(p+1)) && ispseudoprime(pr+nextprime(p+1)), print1(p, ", "))) \\ Felix Fröhlich, Sep 20 2019
A087715
Table read by rows where i-th row consists of primes P of the form P=j*P(i)# -1 or P=j*P(i)# +1 with 0 < j < P(i+1). Here P(r)# = A002110.
Original entry on oeis.org
3, 3, 5, 5, 7, 11, 13, 17, 19, 23, 29, 31, 59, 61, 89, 149, 151, 179, 181, 211, 419, 421, 631, 839, 1049, 1051, 1259, 1471, 1889, 2099, 2309, 2311, 4621, 9239, 9241, 11549, 11551, 13859, 18481, 20789, 23099, 25409, 25411, 30029, 90089, 120121, 150151
Offset: 0
Table begins:
3,3,5,
5,7,11,13,17,19,23,
29,31,59,61,89,149,151,179,181,
211,419,421,631,839,1049,1051,1259,1471,1889,2099,
2309,2311,4621,9239,9241,11549,11551,13859,18481,20789,23099,25409,25411
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{for(i=1,6, p=prod(j=1,i, prime(j)); for(j=1, prime(i+1)-1, c=j*p; if(isprime(c-1),print1(c-1 ",")); if(isprime(c+1),print1(c+1 ",")); ););}
A087728
Table read by rows where i-th row consists of primes P of the form P=(j*P(i)#)^2 +1 with 0 < j < P(i+1). Here P(i)# = A002110(i).
Original entry on oeis.org
5, 17, 37, 577, 8101, 14401, 22501, 32401, 44101, 176401, 5336101, 48024901, 85377601, 341510401, 533610001, 129859329601, 12770402544901, 16679709446401, 94083986096101, 6021375110150401, 11384162317628101
Offset: 0
Table begins:
5,17,
37,577,
8101,14401,22501,32401,
44101,176401,
5336101,48024901,85377601,341510401,533610001,
129859329601,
12770402544901,16679709446401
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{for(i=1,8, p=prod(j=1,i, prime(j)); for(j=1, prime(i+1)-1, c=(j*p)^2+1; if(isprime(c),print1(c ",")); ););}
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