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 ",")); ););}
A087716
Base-2 pseudoprimes (see A001567) of the form j*p(i)# - p(k) or j*p(i)# + p(k), p(i) and p(k) primes with p(i) < p(k) < p(i+1)^2 and 0 < j < p(i+1).
Original entry on oeis.org
341, 1387, 2047, 4681, 13747
Offset: 1
2*7# - 79 = 341,
7*7# - 83 = 1387,
10*7# - 53 = 2047,
2*11# + 61 = 4681,
6*11# - 113 = 13747,
13*7# - 29 = 2701.
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lst(lim)=my(p=2,P=1,v=List());forprime(q=3,lim,P*=p;forprime(r=q, q^2, for(j=1,q-1,if(j*P-r>340&&psp(j*P-r),listput(v,j*P-r)); if(psp(j*P+r),listput(v,j*P+r))));p=q);vecsort(Vec(v),,8) \\ Charles R Greathouse IV, Apr 12 2012
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 ",")); ););}
A088415
Primes p = prime(i) such that p(i)# - p(i+1) or p(i)# + p(i+1) or both are primes.
Original entry on oeis.org
2, 3, 5, 7, 11, 13, 17, 19, 43, 53, 59, 73, 79, 83, 89, 149, 367, 431, 853, 4007, 6143, 8819, 8969
Offset: 1
3=p(2) is in the sequence because p(2)# + p(3) = 11 is prime.
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Do[ p = Product[Prime[i], {i, 1, n}]; q = Prime[n + 1]; If[ PrimeQ[p - q] || PrimeQ[p + q], Print[ Prime[n]]], {n, 1, 1435}]
A093078
Primes p = prime(i) such that p(i)# - p(i+1) is prime.
Original entry on oeis.org
5, 7, 11, 13, 19, 79, 83, 89, 149, 367, 431, 853, 4007, 8819, 8969, 12953, 18301, 18869
Offset: 1
3 = p(2) is in the sequence because p(2)# + p(3) = 11 is prime.
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Do[p = Product[ Prime[i], {i, 1, n}]; q = Prime[n + 1]; If[ PrimeQ[p - q], Print[ Prime[n]]], {n, 1, 1435}]
Module[{nn=1120,pr1,pr2,prmrl},pr1=Prime[Range[nn]];pr2=Prime[Range[ 2, nn+1]]; prmrl=FoldList[Times,pr1];Transpose[Select[Thread[{pr1,pr2, prmrl}], PrimeQ[#[[3]]-#[[2]]]&]][[1]]] (* Harvey P. Dale, Dec 07 2015 *)
n=1;Monitor[Parallelize[While[True,If[PrimeQ[Product[Prime[k],{k,1,n}]-Prime[n + 1]],Print[Prime[n]]];n++];n],n] (* J.W.L. (Jan) Eerland, Dec 19 2022 *)
A093077
Primes p = prime(i) such that p(i)# + p(i+1) is prime.
Original entry on oeis.org
2, 3, 5, 13, 17, 19, 43, 53, 59, 73, 367, 6143
Offset: 1
3 = p(2) is in the sequence because p(2)# + p(3) = 11 is prime.
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Do[p = Product[ Prime[i], {i, 1, n}]; q = Prime[n + 1]; If[ PrimeQ[p + q], Print[ Prime[n]]], {n, 1, 1435}]
With[{nn=1000},NextPrime[#,-1]&/@(Select[Thread[{FoldList[ Times,Prime[ Range[nn]]],Prime[Range[ 2,nn+1]]}], PrimeQ[ Total[#]]&][[All,2]])] (* Harvey P. Dale, Oct 07 2018 *)
Showing 1-6 of 6 results.
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