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Block #264,475

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/18/2013, 5:30:23 PM Β· Difficulty 9.9644 Β· 6,536,688 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
331d08068268b09eb64570e718736fdb7694363b49bb6456668253dcfc040461
View on Chainz β†—

Height

#264,475

Difficulty

9.964378

Transactions

1

Size

208 B

Version

2

Bits

09f6e178

Nonce

51,658

Timestamp

11/18/2013, 5:30:23 PM

Confirmations

6,536,688

Merkle Root

b32627573a60e1010c29d3b3b32b0185b5fde25322fe3b2ba40761dbc3ccc6a1
Transactions (1)
Coinbaseb32627573a60e1…0761dbc3ccc6a1
1 in β†’ 1 out10.0600 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.

6.068 Γ— 10⁹⁸(99-digit number)
60681461711325509120…39344877677886467360
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
6.068 Γ— 10⁹⁸(99-digit number)
60681461711325509120…39344877677886467359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.068 Γ— 10⁹⁸(99-digit number)
60681461711325509120…39344877677886467361
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
1.213 Γ— 10⁹⁹(100-digit number)
12136292342265101824…78689755355772934719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.213 Γ— 10⁹⁹(100-digit number)
12136292342265101824…78689755355772934721
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
2.427 Γ— 10⁹⁹(100-digit number)
24272584684530203648…57379510711545869439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.427 Γ— 10⁹⁹(100-digit number)
24272584684530203648…57379510711545869441
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
4.854 Γ— 10⁹⁹(100-digit number)
48545169369060407296…14759021423091738879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.854 Γ— 10⁹⁹(100-digit number)
48545169369060407296…14759021423091738881
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
9.709 Γ— 10⁹⁹(100-digit number)
97090338738120814592…29518042846183477759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.709 Γ— 10⁹⁹(100-digit number)
97090338738120814592…29518042846183477761
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 264475

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 331d08068268b09eb64570e718736fdb7694363b49bb6456668253dcfc040461

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 #264,475 on Chainz β†—
Circulating Supply:57,653,364 XPMΒ·at block #6,801,162 Β· updates every 60s
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