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Block #443,131

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/14/2014, 8:33:05 AM Β· Difficulty 10.3440 Β· 6,381,463 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1f097a83c73baf8cfb2636fa4806f792d9e6d34a7aca993cf2b01b70b080a9f1
View on Chainz β†—

Height

#443,131

Difficulty

10.343980

Transactions

1

Size

221 B

Version

2

Bits

0a580f17

Nonce

140,006

Timestamp

3/14/2014, 8:33:05 AM

Confirmations

6,381,463

Merkle Root

98ae8c6288bb3c32d7dbe20e9f799f24f8a7981bd663e7ba154a18d2cac0354a
Transactions (1)
Coinbase98ae8c6288bb3c…4a18d2cac0354a
1 in β†’ 2 out9.3300 XPM131 B
AMVf7Jrg…xd5AVR7CAJno7LX2…vo4wdWtY
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.

1.293 Γ— 10⁹⁡(96-digit number)
12939439776805711407…20409765451120046980
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
1.293 Γ— 10⁹⁡(96-digit number)
12939439776805711407…20409765451120046979
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.293 Γ— 10⁹⁡(96-digit number)
12939439776805711407…20409765451120046981
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
2.587 Γ— 10⁹⁡(96-digit number)
25878879553611422815…40819530902240093959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.587 Γ— 10⁹⁡(96-digit number)
25878879553611422815…40819530902240093961
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
5.175 Γ— 10⁹⁡(96-digit number)
51757759107222845630…81639061804480187919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.175 Γ— 10⁹⁡(96-digit number)
51757759107222845630…81639061804480187921
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
1.035 Γ— 10⁹⁢(97-digit number)
10351551821444569126…63278123608960375839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.035 Γ— 10⁹⁢(97-digit number)
10351551821444569126…63278123608960375841
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
2.070 Γ— 10⁹⁢(97-digit number)
20703103642889138252…26556247217920751679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.070 Γ— 10⁹⁢(97-digit number)
20703103642889138252…26556247217920751681
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 443131

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 1f097a83c73baf8cfb2636fa4806f792d9e6d34a7aca993cf2b01b70b080a9f1

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 #443,131 on Chainz β†—
Circulating Supply:57,840,821 XPMΒ·at block #6,824,593 Β· updates every 60s
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