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Block #376,836

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/26/2014, 4:30:38 PM Β· Difficulty 10.4252 Β· 6,417,777 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b38875ea72633141482c6847e47a6041f57cb6aa79e084d6af1ca815352cb20d
View on Chainz β†—

Height

#376,836

Difficulty

10.425207

Transactions

2

Size

363 B

Version

2

Bits

0a6cda5f

Nonce

1,564

Timestamp

1/26/2014, 4:30:38 PM

Confirmations

6,417,777

Merkle Root

8d08db5227a7e4630d66a96273d9ecc2ca05209cc58c3615d3eed13c03bf8844
Transactions (2)
Coinbasedfdf15c0048ac5…c8de24cd0d55bd
1 in β†’ 1 out9.2000 XPM116 B
AbwWkWZt…kawDhufa
0b06571dc3d0d9…3e2dbfd11e9fef
1 in β†’ 1 out9.1700 XPM157 B
AUBJWpeh…Y625Gjnz
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.

2.269 Γ— 10⁹⁡(96-digit number)
22695426176780259991…29078323698653350740
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
2.269 Γ— 10⁹⁡(96-digit number)
22695426176780259991…29078323698653350739
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.269 Γ— 10⁹⁡(96-digit number)
22695426176780259991…29078323698653350741
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
4.539 Γ— 10⁹⁡(96-digit number)
45390852353560519983…58156647397306701479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.539 Γ— 10⁹⁡(96-digit number)
45390852353560519983…58156647397306701481
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
9.078 Γ— 10⁹⁡(96-digit number)
90781704707121039967…16313294794613402959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.078 Γ— 10⁹⁡(96-digit number)
90781704707121039967…16313294794613402961
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
1.815 Γ— 10⁹⁢(97-digit number)
18156340941424207993…32626589589226805919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.815 Γ— 10⁹⁢(97-digit number)
18156340941424207993…32626589589226805921
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
3.631 Γ— 10⁹⁢(97-digit number)
36312681882848415986…65253179178453611839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.631 Γ— 10⁹⁢(97-digit number)
36312681882848415986…65253179178453611841
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 376836

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 b38875ea72633141482c6847e47a6041f57cb6aa79e084d6af1ca815352cb20d

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 #376,836 on Chainz β†—
Circulating Supply:57,600,947 XPMΒ·at block #6,794,612 Β· updates every 60s
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