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Block #324,011

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/22/2013, 1:02:56 AM Β· Difficulty 10.2075 Β· 6,471,327 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b5443f08ad1a4c2bfa94bb22eca71422bfa931c059c0e2bdceeb688c044dd8b6
View on Chainz β†—

Height

#324,011

Difficulty

10.207502

Transactions

1

Size

210 B

Version

2

Bits

0a351ed7

Nonce

15,232

Timestamp

12/22/2013, 1:02:56 AM

Confirmations

6,471,327

Merkle Root

72a16e2e33d0fed3a86e28b8599320b32b3cc5c05424eeb3d94007f690aba67a
Transactions (1)
Coinbase72a16e2e33d0fe…4007f690aba67a
1 in β†’ 1 out9.5800 XPM116 B
AbwWkWZt…kawDhufa
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.

1.662 Γ— 10¹⁰³(104-digit number)
16621440111105370940…68755969558818324480
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
1.662 Γ— 10¹⁰³(104-digit number)
16621440111105370940…68755969558818324479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.662 Γ— 10¹⁰³(104-digit number)
16621440111105370940…68755969558818324481
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
3.324 Γ— 10¹⁰³(104-digit number)
33242880222210741881…37511939117636648959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.324 Γ— 10¹⁰³(104-digit number)
33242880222210741881…37511939117636648961
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
6.648 Γ— 10¹⁰³(104-digit number)
66485760444421483762…75023878235273297919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.648 Γ— 10¹⁰³(104-digit number)
66485760444421483762…75023878235273297921
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
1.329 Γ— 10¹⁰⁴(105-digit number)
13297152088884296752…50047756470546595839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.329 Γ— 10¹⁰⁴(105-digit number)
13297152088884296752…50047756470546595841
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
2.659 Γ— 10¹⁰⁴(105-digit number)
26594304177768593504…00095512941093191679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.659 Γ— 10¹⁰⁴(105-digit number)
26594304177768593504…00095512941093191681
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 324011

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 b5443f08ad1a4c2bfa94bb22eca71422bfa931c059c0e2bdceeb688c044dd8b6

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 #324,011 on Chainz β†—
Circulating Supply:57,606,763 XPMΒ·at block #6,795,337 Β· updates every 60s
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