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Block #30,431

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2013, 7:05:14 PM Β· Difficulty 7.9869 Β· 6,794,962 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9f3a2fd25ba38e5b434439a59060de3cbc6e8419eaa6ea6eab66a33f331b6159
View on Chainz β†—

Height

#30,431

Difficulty

7.986853

Transactions

1

Size

199 B

Version

2

Bits

07fca26b

Nonce

483

Timestamp

7/13/2013, 7:05:14 PM

Confirmations

6,794,962

Merkle Root

04497ed3f9e1563896d763675749755505a0e6b19cd94c4e33c623224a04be2f
Transactions (1)
Coinbase04497ed3f9e156…c623224a04be2f
1 in β†’ 1 out15.6600 XPM109 B
AZimcBDq…wdQoGBMh
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.

7.887 Γ— 10⁹⁡(96-digit number)
78873885923276437204…88506860202905204430
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
7.887 Γ— 10⁹⁡(96-digit number)
78873885923276437204…88506860202905204429
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.887 Γ— 10⁹⁡(96-digit number)
78873885923276437204…88506860202905204431
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
1.577 Γ— 10⁹⁢(97-digit number)
15774777184655287440…77013720405810408859
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.577 Γ— 10⁹⁢(97-digit number)
15774777184655287440…77013720405810408861
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
3.154 Γ— 10⁹⁢(97-digit number)
31549554369310574881…54027440811620817719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.154 Γ— 10⁹⁢(97-digit number)
31549554369310574881…54027440811620817721
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
6.309 Γ— 10⁹⁢(97-digit number)
63099108738621149763…08054881623241635439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.309 Γ— 10⁹⁢(97-digit number)
63099108738621149763…08054881623241635441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8
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 30431

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 9f3a2fd25ba38e5b434439a59060de3cbc6e8419eaa6ea6eab66a33f331b6159

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 #30,431 on Chainz β†—
Circulating Supply:57,847,243 XPMΒ·at block #6,825,392 Β· updates every 60s
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