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Block #232,466

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/29/2013, 3:27:28 AM Β· Difficulty 9.9410 Β· 6,593,763 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5496f666df7b747a3e65649f8e3aa7245afe88421457536da186abca1109cc2a
View on Chainz β†—

Height

#232,466

Difficulty

9.941037

Transactions

1

Size

207 B

Version

2

Bits

09f0e7c8

Nonce

2,654

Timestamp

10/29/2013, 3:27:28 AM

Confirmations

6,593,763

Merkle Root

f76988bcfdff3dfd4af2e8d28b8672d6ee7bb9779d0277fac52c4280b191deea
Transactions (1)
Coinbasef76988bcfdff3d…2c4280b191deea
1 in β†’ 1 out10.1000 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.328 Γ— 10⁹⁢(97-digit number)
13282125689833355246…90895191409410884000
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
1.328 Γ— 10⁹⁢(97-digit number)
13282125689833355246…90895191409410883999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.328 Γ— 10⁹⁢(97-digit number)
13282125689833355246…90895191409410884001
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
2.656 Γ— 10⁹⁢(97-digit number)
26564251379666710492…81790382818821767999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.656 Γ— 10⁹⁢(97-digit number)
26564251379666710492…81790382818821768001
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
5.312 Γ— 10⁹⁢(97-digit number)
53128502759333420984…63580765637643535999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.312 Γ— 10⁹⁢(97-digit number)
53128502759333420984…63580765637643536001
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
1.062 Γ— 10⁹⁷(98-digit number)
10625700551866684196…27161531275287071999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.062 Γ— 10⁹⁷(98-digit number)
10625700551866684196…27161531275287072001
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
2.125 Γ— 10⁹⁷(98-digit number)
21251401103733368393…54323062550574143999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9
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 232466

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 5496f666df7b747a3e65649f8e3aa7245afe88421457536da186abca1109cc2a

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 #232,466 on Chainz β†—
Circulating Supply:57,853,966 XPMΒ·at block #6,826,228 Β· updates every 60s
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