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Block #792,072

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/1/2014, 11:10:56 AM Β· Difficulty 10.9734 Β· 6,003,319 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
a2c9d62b305520bb8b76ffde28e95812bf6a00e70d88ba810fbbca7e42deb880
View on Chainz β†—

Height

#792,072

Difficulty

10.973437

Transactions

1

Size

207 B

Version

2

Bits

0af93326

Nonce

479,847,767

Timestamp

11/1/2014, 11:10:56 AM

Confirmations

6,003,319

Merkle Root

5f1a14911d0805c85f94bffdcd2b167652fb015e7383e8a14a805aa07a49c275
Transactions (1)
Coinbase5f1a14911d0805…805aa07a49c275
1 in β†’ 1 out8.2900 XPM116 B
ANSXnLY2…Sd25TjkD
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.355 Γ— 10⁹⁷(98-digit number)
13552423062144296498…95081158836888330240
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.355 Γ— 10⁹⁷(98-digit number)
13552423062144296498…95081158836888330239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.355 Γ— 10⁹⁷(98-digit number)
13552423062144296498…95081158836888330241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
2.710 Γ— 10⁹⁷(98-digit number)
27104846124288592996…90162317673776660479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.710 Γ— 10⁹⁷(98-digit number)
27104846124288592996…90162317673776660481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
5.420 Γ— 10⁹⁷(98-digit number)
54209692248577185992…80324635347553320959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.420 Γ— 10⁹⁷(98-digit number)
54209692248577185992…80324635347553320961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.084 Γ— 10⁹⁸(99-digit number)
10841938449715437198…60649270695106641919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.084 Γ— 10⁹⁸(99-digit number)
10841938449715437198…60649270695106641921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.168 Γ— 10⁹⁸(99-digit number)
21683876899430874397…21298541390213283839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.168 Γ— 10⁹⁸(99-digit number)
21683876899430874397…21298541390213283841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
4.336 Γ— 10⁹⁸(99-digit number)
43367753798861748794…42597082780426567679
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 792072

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock a2c9d62b305520bb8b76ffde28e95812bf6a00e70d88ba810fbbca7e42deb880

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #792,072 on Chainz β†—
Circulating Supply:57,607,188 XPMΒ·at block #6,795,390 Β· updates every 60s
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