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Home/Chain Registry/Block #2,272,063

Block #2,272,063

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/28/2017, 4:04:39 PM Β· Difficulty 10.9540 Β· 4,571,014 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a7ba184e456f3f3cbb4c3fc09b0471d353c4cd7e66eae3458e300253c56e1f3f
View on Chainz β†—

Difficulty

10.953987

Transactions

1

Size

200 B

Version

2

Bits

0af4387c

Nonce

607,601,121

Timestamp

8/28/2017, 4:04:39 PM

Confirmations

4,571,014

Merkle Root

29b692f63b2af7fdbbb7f7acf0be5475857fd23d2d5f4f10c8676eb35f34bdfe
Transactions (1)
Coinbase29b692f63b2af7…676eb35f34bdfe
1 in β†’ 1 out8.3200 XPM110 B
AbGhKQJx…5XGpZTxN
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.

2.804 Γ— 10⁹⁡(96-digit number)
28044506868710509172…42654377138996183680
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
2.804 Γ— 10⁹⁡(96-digit number)
28044506868710509172…42654377138996183679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.804 Γ— 10⁹⁡(96-digit number)
28044506868710509172…42654377138996183681
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
5.608 Γ— 10⁹⁡(96-digit number)
56089013737421018345…85308754277992367359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.608 Γ— 10⁹⁡(96-digit number)
56089013737421018345…85308754277992367361
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
1.121 Γ— 10⁹⁢(97-digit number)
11217802747484203669…70617508555984734719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.121 Γ— 10⁹⁢(97-digit number)
11217802747484203669…70617508555984734721
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
2.243 Γ— 10⁹⁢(97-digit number)
22435605494968407338…41235017111969469439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.243 Γ— 10⁹⁢(97-digit number)
22435605494968407338…41235017111969469441
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
4.487 Γ— 10⁹⁢(97-digit number)
44871210989936814676…82470034223938938879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.487 Γ— 10⁹⁢(97-digit number)
44871210989936814676…82470034223938938881
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
8.974 Γ— 10⁹⁢(97-digit number)
89742421979873629352…64940068447877877759
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 2272063

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 a7ba184e456f3f3cbb4c3fc09b0471d353c4cd7e66eae3458e300253c56e1f3f

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 #2,272,063 on Chainz β†—
Circulating Supply:57,988,976 XPMΒ·at block #6,843,076 Β· updates every 60s
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