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Block #339,579

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/2/2014, 5:20:06 AM Β· Difficulty 10.1254 Β· 6,491,308 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b6a6c028256457107221e6e2bcf3cdbf5140944d75a0a353adecf7bf27258aca
View on Chainz β†—

Height

#339,579

Difficulty

10.125385

Transactions

1

Size

211 B

Version

2

Bits

0a201934

Nonce

127,113

Timestamp

1/2/2014, 5:20:06 AM

Confirmations

6,491,308

Merkle Root

e8a9b39aa4f5328b1a0cec4f9a1df3d306df1511db696958065d729afacbadb6
Transactions (1)
Coinbasee8a9b39aa4f532…5d729afacbadb6
1 in β†’ 1 out9.7400 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.

1.110 Γ— 10¹⁰⁷(108-digit number)
11103941912653368423…17194195655799168000
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
1.110 Γ— 10¹⁰⁷(108-digit number)
11103941912653368423…17194195655799167999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.110 Γ— 10¹⁰⁷(108-digit number)
11103941912653368423…17194195655799168001
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
2.220 Γ— 10¹⁰⁷(108-digit number)
22207883825306736846…34388391311598335999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.220 Γ— 10¹⁰⁷(108-digit number)
22207883825306736846…34388391311598336001
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
4.441 Γ— 10¹⁰⁷(108-digit number)
44415767650613473692…68776782623196671999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.441 Γ— 10¹⁰⁷(108-digit number)
44415767650613473692…68776782623196672001
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
8.883 Γ— 10¹⁰⁷(108-digit number)
88831535301226947384…37553565246393343999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.883 Γ— 10¹⁰⁷(108-digit number)
88831535301226947384…37553565246393344001
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
1.776 Γ— 10¹⁰⁸(109-digit number)
17766307060245389476…75107130492786687999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.776 Γ— 10¹⁰⁸(109-digit number)
17766307060245389476…75107130492786688001
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 339579

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 b6a6c028256457107221e6e2bcf3cdbf5140944d75a0a353adecf7bf27258aca

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 #339,579 on Chainz β†—
Circulating Supply:57,891,233 XPMΒ·at block #6,830,886 Β· updates every 60s
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