We have some very large papaya. They are called watermelon papaya and can grow larger than a football. Usually the really big ones are on trees that don't have a lot of crowded fruit. Very large fruit are usually female and if underpolinated they won't have a lot of seeds. My dad had one one time that had 2 seeds.
Most fruit from female trees will fall if not polinated but on occasion a female tree will be able to get mature fruit but the clue would be the lack of seeds.
You cannot tell if your tree is male, female or hermaphrodite until it is 5 months old and has started to flower. Ignore the first flowers because there will be a lot of males and few females. (no fruit in the flower). It is natural, but does not necessarily mean you have a male tree. Hermaphrodites will produce male flowers first.
Sunrise and X77 (Waimanalo low bearing) are non-GMO cultivars. They are solo type papaya. Rainbow is GMO and is widely sold in most markets here and on the mainland. It is a sweet yellow fleshed fruit that is resistant to papaya ringspot virus.
Sometimes I can get these to grow at my house but they don't survive at the community garden. There is an easy test available now to test for GMO contamination. The leaf is tested for the gene. There are people who still don't want to eat GMO fruit by choice and others by sheer ignorance. Most papaya grown in backyards here are from saved seeds or seeds from unknown varieties. Most people don't care about the pedigree if it tastes good. The one bad things about the purists are that if you want a pure variety, you will have to isolate and rogue out any trees the birds bring. GMO papaya will cross with any other papaya and papaya are polinated by insects so it is not uncommon for someone to unknowingly be growing a GMO papaya. My friend, touted the fact that his non-GMO (unknown) papaya was growing next to his neighbor's obviously infested plant and remained healthy. I think if he tested that tree, odds are his papaya had the PRSV resistant gene.
I grow mostly GMO papaya because there are squash all around me. Papaya ringspot virus is thought to be a mutated version of a squash virus that jumped hosts. Squash may be asymptomatic hosts of PRSV. My neighbor does not cut down his infested tree so the only ones that will survive have to have GMO genes. GMO papaya have been around since 1998 and are perfectly safe to eat. I prefer Malaysian papaya but they are not ringspot resistant. I had 5 trees at one time and my mother came and raided them regularly even though she had her own trees. I tried to plant more but because of the neighbor's infested tree they all got the virus early and I had to cut them down.
The GMO modification was the insertion of a gene that coats the virus and prevents it from causing the disease.
Papaya ringspot virus is a problem worldwide and other countries are also looking at GMO techniques to save their livelihoods. GMO techniques were developed to make life easier for people not to harm them.
https://www.biofortified.org/2014/03/gm ... ut-people/
Happy gardening in Hawaii. Gardens are where people grow.