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A112418
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Primes which have a prime number of partitions into five distinct primes.
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1
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53, 59, 67, 83, 113, 151, 157, 211, 239, 601, 809, 821, 881, 971, 1237, 1297, 1427, 1669, 1759, 1973, 2069, 2129, 2243, 2333, 2659, 2677, 2719, 2789, 2803, 2999, 3329, 3613, 3623, 3769, 3797, 4001, 4451
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OFFSET
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1,1
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COMMENTS
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The corresponding numbers of partitions are 2,5,11,29,109,331,379,1091...
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LINKS
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EXAMPLE
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53 is there because there are 2 partitions of 53 (3+7+11+13+19, 5+7+11+13+17) and 2 is prime.
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MAPLE
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part5_prime:=proc(N) s:=1; for n from 2 to N do cont:=0; for i from 1 to n-5 do for j from i+1 to n-4 do for k from j+1 to n-3 do for l from k+1 to n-2 do for m from l+1 to n-1 do if(ithprime(n)= ithprime(i)+ithprime(j)+ithprime(k)+ithprime(l)+ithprime(m) then cont:=cont+1; fi; od; od; od; od; od; if (isprime(cont)=true) then a[s]:=ithprime(n); s:=s+1; fi; od; end:
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PROG
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(PARI) has(n)=my(t, Q, R, S); forprime(p=n\5+1, n-26, Q=n-p; forprime(q=Q\4+1, min(p-1, Q-15), R=Q-q; forprime(r=R\3+1, min(q-1, R-8), S=R-r; forprime(s=S-r+1, (S-1)\2, isprime(S-s) && t++)))); isprime(t)
(PARI) list(lim)=my(v=vectorsmall(precprime(lim)), u=List(), Q, R, S); forprime(p=13, #v-26, Q=#v-p; forprime(q=11, min(p-1, Q-15), R=Q-q; forprime(r=7, min(q-1, R-8), S=R-r; forprime(s=5, min(S-2, r-1), forprime(t=3, min(S-s, s-1), v[p+q+r+s+t]++))))); forprime(p=2, lim, if(isprime(v[p]), listput(u, p))); Set(u) \\ Charles R Greathouse IV, Apr 22 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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