His birth and christening on FamilySearch:

name: Jeremiah Bartholomew
gender: Male
baptism/christening date: 17 Dec 1819
baptism/christening place: Suffolk, England
birth date: 13 Dec 1819
father's name: William Bartholomew
mother's name: Mary Moore Bartholomew
indexing project (batch) number: C01682-1
system origin: England-EASy
source film number: 951466
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At marriage his name was spelled Bartholemew and was eventually found.
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In 1861:

Surname  Forename  Age  Relation  Occupation  Birth Place

Bartholomew Jeremiah 40 Head Ag Labourer Bury St Edmunds, Suffolk
Bartholomew Eliza 33 Wife Ag Labourer Gareley,
Bartholomew Jonathan 8 Son Ag Labourer Kentford, Suffolk
Bartholomew Jane 7 Daughter Ag Labourer Kentford, Suffolk
Bartholomew James 5 Son Ag Labourer Kentford, Suffolk
Bartholomew Betsy 3 Daughter Ag Labourer Kentford, Suffolk
Bartholomew William 1 Son Ag Labourer  Kentford, Suffolk
Wright Anne 70 Nephew Widow Shepperd Widow  Dalham, Suffolk

Ref: RG9/1142/~F47

Address: Gateley Place
Parish: Kentford
Registration District: Mildenhall

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This looks like his death:

Surname   First name(s)   Age   District   Vol  Page
Deaths Sep 1864   (>99%)
Bartholomew Jeremiah Mildenhall 4a 323
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After his death his wife remarried and in the 1871 census all their children were recorded with the name of her new husband, just to confuse.  The last two were the progeny of Eliza and her new husband:

Surname  Forename  Age  Relation  Occupation  Birth Place

Nunn Edward 41  Head   Agricultural Labourer Moulton, Suffolk
Nunn Eliza 44  Wife Gazeley, Suffolk
Nunn James B  15  Son Agricultural Labourer Kentford, Suffolk
Nunn Betsy 13 Daughter Kentford, Suffolk
Nunn William 11 Son Kentford, Suffolk
Nunn Margaret 8 Daughter Kentford, Suffolk
Nunn Jeremiah 6 Son Kentford, Suffolk
Nunn Lydia 2 Daughter Kentford, Suffolk
Nunn Samuel 10 M Son Kentford, Suffolk

Ref: RG10/1599/F?

Address: Well Bottom Cottages
Parish: Moulton
Registration District: Newmarket
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Their marriage registration:

Surname   First name(s)      District   Vol  Page
Marriages Jun 1851   (>99%)
Bartholemew Jeremiah Mildenhall 13 719
PRIGG Eliza    Mildenhall 13 719
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