, ▁ 2 9 ) ▁and ▁( 5 , ▁ 7 , ▁ 1 3 , ▁ 1 9 , ▁ 3 1 ) ▁where ▁all ▁con gru ences ▁( mod ▁ 5 ) ▁are ▁included ▁in ▁both ▁cases . ▁ ▁Prime ▁const ell ations ▁The ▁diameter ▁of ▁a ▁k - tuple ▁is ▁the ▁difference ▁of ▁its ▁largest ▁and ▁smallest ▁elements . ▁An ▁adm iss ible ▁prime ▁k - tuple ▁with ▁the ▁smallest ▁possible ▁diameter ▁d ▁( am ong ▁all ▁adm iss ible ▁k - tu ples ) ▁is ▁a ▁prime ▁const ell ation . ▁For ▁all ▁n   ≥   k ▁this ▁will ▁always ▁produce ▁consecutive ▁pr imes . ▁ ▁This ▁means ▁that , ▁for ▁large ▁n : ▁ ▁p ▁− ▁p ▁ ≥ ▁d ▁ ▁where ▁p ▁is ▁the ▁n th ▁prime . ▁ ▁The ▁first ▁few ▁prime ▁const ell ations ▁are : ▁ ▁The ▁diameter ▁d ▁as ▁a ▁function ▁of ▁k ▁is ▁sequence ▁A 0 0 8 4 0 7 ▁in ▁O E IS . ▁ ▁A ▁prime ▁const ell ation ▁is ▁sometimes ▁referred ▁to ▁as ▁a ▁prime ▁k - tuple t , ▁but ▁some ▁authors ▁reserve ▁that ▁term ▁for ▁instances ▁that ▁are ▁not ▁part ▁of ▁longer ▁k - tuple ts . ▁ ▁The ▁first ▁Hard y – L ittle wood ▁conject ure ▁predict s ▁that ▁the ▁asympt otic ▁frequency ▁of ▁any ▁prime ▁const ell ation ▁can ▁be ▁calculated . ▁ ▁While ▁the ▁conject ure ▁is ▁un pro ven ▁it ▁is ▁considered ▁likely ▁to ▁be ▁true . ▁If ▁that ▁is