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Home/Chain Registry/Block #2,311,906

Block #2,311,906

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/27/2017, 9:40:16 PM Β· Difficulty 10.9064 Β· 4,530,598 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c12cbf7377239e1d284fc3e5cfa9eb6b6e5566ae2b34968baddefad827774c47
View on Chainz β†—

Difficulty

10.906394

Transactions

1

Size

201 B

Version

2

Bits

0ae80968

Nonce

989,541,334

Timestamp

9/27/2017, 9:40:16 PM

Confirmations

4,530,598

Merkle Root

3123ced2fe5a9f766d9cf0eda78c563157ca4a0fcab4664b0399dfdde6a25b94
Transactions (1)
Coinbase3123ced2fe5a9f…99dfdde6a25b94
1 in β†’ 1 out8.3900 XPM110 B
ASPpVpHK…Vn8dZCKU
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.

4.937 Γ— 10⁹⁷(98-digit number)
49378623800404342332…79317241629826498560
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
4.937 Γ— 10⁹⁷(98-digit number)
49378623800404342332…79317241629826498559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.937 Γ— 10⁹⁷(98-digit number)
49378623800404342332…79317241629826498561
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
9.875 Γ— 10⁹⁷(98-digit number)
98757247600808684664…58634483259652997119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.875 Γ— 10⁹⁷(98-digit number)
98757247600808684664…58634483259652997121
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
1.975 Γ— 10⁹⁸(99-digit number)
19751449520161736932…17268966519305994239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.975 Γ— 10⁹⁸(99-digit number)
19751449520161736932…17268966519305994241
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
3.950 Γ— 10⁹⁸(99-digit number)
39502899040323473865…34537933038611988479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.950 Γ— 10⁹⁸(99-digit number)
39502899040323473865…34537933038611988481
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
7.900 Γ— 10⁹⁸(99-digit number)
79005798080646947731…69075866077223976959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.900 Γ— 10⁹⁸(99-digit number)
79005798080646947731…69075866077223976961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2311906

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 c12cbf7377239e1d284fc3e5cfa9eb6b6e5566ae2b34968baddefad827774c47

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 #2,311,906 on Chainz β†—
Circulating Supply:57,984,450 XPMΒ·at block #6,842,503 Β· updates every 60s
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