I saw a Iowa connection for these and looked further: I blieve your Jerimiah born 1836 Ohio and Aaron born 1834 are the ones that moved to Illinois and married: Aaron R. Purdum married Louisa Woodward mercer County, Ill 11-27-1858 vol. 0081 Lic # 00001191,Jeremiah H. Purdum marred Emelene Mc Clure mercer cnty, 1-18-1860 lic # 00001332. now. Arron R. Purdum ( Arron Richard Purdum)and wife is found in 1870 Uniton twp, Cromwell town adams Co., Iowa with wife Louisa born Penn, son Hamlin age 9,duaghter Mary age 6 ,Jeremiah age 4, and Dell(daughter) age 2 all children showing being born in Ill. 1880 Iowa Adams Co., Jasper twp. E/d 13 Aaron Purdum with Louisa the first four children above and new ones, Lola age 8, Elizabeth age 6, Herman age 3, Richard age 1 Jerimiah Purdum brother to Arron is found with wife int the 1860 census. Ill P.O. box KEithsburg. Ill pg 731 603/Purdum, Jerimiahage 24farmer born Ohio , Emiline age 18born Indiana no children Now Hamilin above son of Aaron is found in the 1910 census: Grnt Twp Iowa Adams co., E/d 4 Sheet 3A 40/40Purdum, H.head 49 married once 27 yers 8 of 5 children;farmer born Ill, parents father Oh andmom oh(?) wife: Maryage 49born Ohparents Virg, VErmont son: Richard age 18 born Iowa daug: Ruth age 6 born Iowa Hamlin son Richard died in CAlifornia( Hemet< Ironic because that is where I live)( is really Aaron Richard Ancestry.com shows Iowa cemetery Records Aaron Richard Purdum: born: 15 Oc 1835 die 7 feb 1913 Prairie Rose, Japer town,Lot 86,(Co., K. 102 Reg. Ill. Inf.)first wife buried there:Louisa Purdum born 1842 died 1884 lot 86 wif of A.R., second wife buried there Malinda born 1835 died 1898 wife of A.R.
Hamlain Purdum born 1860 died 1938 lot 40, wife: Mary B. Purdum born 1860 died 1930 lot 40 another Purdum: Glenn Purdum: born 2 Mar 1885 died 2 Apr 1885 lot 85 son of H, and M.B. hope this helps someone.