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Block #265,229

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/19/2013, 9:15:04 AM Β· Difficulty 9.9630 Β· 6,578,233 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ff74f9bf71fde56e95515b36712f5378f25c90b931cabcfc99084dab15961b43
View on Chainz β†—

Height

#265,229

Difficulty

9.963047

Transactions

3

Size

648 B

Version

2

Bits

09f68a40

Nonce

42,547

Timestamp

11/19/2013, 9:15:04 AM

Confirmations

6,578,233

Merkle Root

6e8a3a27250d04d2e3265830f13d4120985a913eb4a04705724424b1916bc6e5
Transactions (3)
Coinbase84478ff2c45c10…b2e589905a8e38
1 in β†’ 2 out10.0800 XPM140 B
AKcbk49N…GJbKa7j1Abiw8n3q…ZnZfgvQW
f406b50f577745…d4bf1c83ed4a7a
1 in β†’ 1 out10.0400 XPM193 B
AREJRekG…a8dWbE8j
376f73101760e0…722dd3b18603a8
1 in β†’ 2 out5.9618 XPM225 B
ALwAo7ze…D795gyvkARo88A54…p5fNN5SA
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.

1.004 Γ— 10⁹⁡(96-digit number)
10046799552567192668…23881530062798514560
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
1.004 Γ— 10⁹⁡(96-digit number)
10046799552567192668…23881530062798514559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.004 Γ— 10⁹⁡(96-digit number)
10046799552567192668…23881530062798514561
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
2.009 Γ— 10⁹⁡(96-digit number)
20093599105134385337…47763060125597029119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.009 Γ— 10⁹⁡(96-digit number)
20093599105134385337…47763060125597029121
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
4.018 Γ— 10⁹⁡(96-digit number)
40187198210268770674…95526120251194058239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.018 Γ— 10⁹⁡(96-digit number)
40187198210268770674…95526120251194058241
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
8.037 Γ— 10⁹⁡(96-digit number)
80374396420537541349…91052240502388116479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.037 Γ— 10⁹⁡(96-digit number)
80374396420537541349…91052240502388116481
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
1.607 Γ— 10⁹⁢(97-digit number)
16074879284107508269…82104481004776232959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.607 Γ— 10⁹⁢(97-digit number)
16074879284107508269…82104481004776232961
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 265229

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 ff74f9bf71fde56e95515b36712f5378f25c90b931cabcfc99084dab15961b43

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 #265,229 on Chainz β†—
Circulating Supply:57,992,065 XPMΒ·at block #6,843,461 Β· updates every 60s
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