"Immortal Genes" common to all organisms?
Introduction
I believe that Sean B. Caroll is confusing:
• the minimum number of genes required for a viable organism
with
• those genes that are present in all organisms — so called ‘immortal genes’
I will deal with each in turn.
The minimum number of genes required for a viable organism
I have not read the book from which the quotation is taken. From its context and my knowledge I think that the author is mistakenly interpreting ‘the minimum number of genes required for a viable organism’ as ‘the genes present in all organisms’. This is because he seems to be referring to work from the laboratory of Craig Ventner on engineering mycoplasma.
Mycoplasma are among the smallest organisms capable of independent life. They have a genome of about 500 coding sequences, but as parasitic organisms they devotes some of these genes to their parasitic mode of life, while they lack others that the host provides.
The number of 500 may actually be too high: a figure of 300 is quoted in this description, who had plans of Ventner’s plans to build an organism containing a minimal genome containing only such essential genes. There is more on this in a Wikipedia article entitled Mycoplasma laboratorium. It should be noted that the word “immortal” does not appear in either account.
‘Les Immortels’ — genes present in all organisms
The poster would like a list of those genes essential to life, but I know of no such list. How would one go about composing one?
First, one has to set the rules. Do parasites, such as mycoplasma, which are dependent on their host organism, count? Do human beings count? We require amino acids and vitamins, but obtain them from food rather than synthesizing them ourselves. So although it is necessary that a self-sufficient organism have the enzymes for synthesizing the 20 amino acids of the genetic code, these are not all present in humans. I would suggest that we have to restrict ‘les immortels’ to self-sufficient organisms.
Second, one has to decide whether one is talking about a set of genes for accomplishing a function, or individual genes with a structural relationship in all living things that suggests a common identity. For example all cellular organisms (i.e. excluding viruses) must have ribosomes to synthesize proteins, but the protein complement of those ribosomes differs among organisms. Thus, the ribosomal proteins necessary to engineer a minimal mycoplasma may differ from those present in a bacterium such as Escherichia coli, and will certainly not be common to humans. I would suggest we would have to go for the latter.
Having made this decision, one  would get a team of undergraduate students to take all the genes in the genome of E. coli (or even of a mycoplasma) and perform BLAST searches to see whether they are present in representative organisms. Unfortunately I am no longer in a position to torment undergraduate students in this way, so I will have to start a list myself and encourage others to add to (or subtract from) it.
The List — a start
The genes for DNA replication, transcription of RNA and protein synthesis constitute the low hanging fruit here. My area is (used to be) protein synthesis, so I will start there:
Protein Synthesis
Large and small subunit and 5S ribosomal RNAs (3)
Ribosomal proteins (≤32)
Protein synthesis factors — EF1, EF2, IF1 and possibly others
Aminoacyl tRNA synthetases (20?)
tRNAs? — but all that is conserved is probably the anticodon (and sometimes not even that)
Accessory enzymes for protein synthesis:
Pseudouridine synthase
rRNA methylases?
DNA synthesis
B-family DNA polymerases?
RNA synthesis
? Evolutionarily related, but complicated because of multi-subunit nature
But if DNA synthesis is a problem, the reactions leading from RNA to DNA are surely not:
Enzymes of nucleotide metabolism
Ribonucleotide reductase (two subunits)
Thymidylate synthase
Uracil DNA-glycosylase?
Tetrahydrofolate reductase?
Enzymes for interconversion of nucleotides — Adenylate kinase? Nucleoside-diphosphate kinase?
Metabolism
This requires some work. One cannot specify either aerobic or anaerobic metabolsm, but in either case one needs oxido-reducto enzymes. Enzymes of hexose metabolism — hexokinase? Enzymes to metabolize key intermediates like glutamate and glutamine, and enzymes for introducing different groups in synthetic processes. This could make an interesting crowd-sourced project, or, failing that, a game for your next Biochemistry Christmas Party.