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Male Israel Palmer Click to view Israel Palmer in the family tree

Israel was born on September 22nd, 1778.1   Israel's father was Asa Palmer and his mother was Susanne Unknown.  His paternal grandparents were Abraham Palmer and Rachel Reynolds. He had five brothers and six sisters, named Richard, Abraham, Asa Parker, James, Nathaniel, Rachel, Hulday, Ruth, Anna, Susanne and Abigail.  He was the oldest of the twelve children. He had three half-brothers and three half-sisters, named Benjamin, Sheldon, Eli, Betsy, Dilly and Lorinda.1 

1 phelps.FTW @ Tree #1309
Further sources/citations:
World Family Tree Vol. 3, Ed. 1 @ Tree #3455, 3455.ftw