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Block #443,137

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/14/2014, 8:40:53 AM Β· Difficulty 10.3438 Β· 6,352,155 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
90cf77cc17798a43e9ebe5cf89e5c1c3a9d757673724378d0aef2ce4c643c705
View on Chainz β†—

Height

#443,137

Difficulty

10.343783

Transactions

1

Size

200 B

Version

2

Bits

0a58022e

Nonce

327,205

Timestamp

3/14/2014, 8:40:53 AM

Confirmations

6,352,155

Merkle Root

aae396c90fd27753d742fd930ea4e102f1b8972f3fc0378f11c4f7601eefee27
Transactions (1)
Coinbaseaae396c90fd277…c4f7601eefee27
1 in β†’ 1 out9.3300 XPM110 B
AeKNrjNj…1NEq95Ta
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.

9.156 Γ— 10⁹⁴(95-digit number)
91561685278956582883…07011803338959779520
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
9.156 Γ— 10⁹⁴(95-digit number)
91561685278956582883…07011803338959779519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.156 Γ— 10⁹⁴(95-digit number)
91561685278956582883…07011803338959779521
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
1.831 Γ— 10⁹⁡(96-digit number)
18312337055791316576…14023606677919559039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.831 Γ— 10⁹⁡(96-digit number)
18312337055791316576…14023606677919559041
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
3.662 Γ— 10⁹⁡(96-digit number)
36624674111582633153…28047213355839118079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.662 Γ— 10⁹⁡(96-digit number)
36624674111582633153…28047213355839118081
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
7.324 Γ— 10⁹⁡(96-digit number)
73249348223165266306…56094426711678236159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.324 Γ— 10⁹⁡(96-digit number)
73249348223165266306…56094426711678236161
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
1.464 Γ— 10⁹⁢(97-digit number)
14649869644633053261…12188853423356472319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.464 Γ— 10⁹⁢(97-digit number)
14649869644633053261…12188853423356472321
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 443137

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 90cf77cc17798a43e9ebe5cf89e5c1c3a9d757673724378d0aef2ce4c643c705

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 #443,137 on Chainz β†—
Circulating Supply:57,606,387 XPMΒ·at block #6,795,291 Β· updates every 60s
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