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Block #442,458

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/13/2014, 8:28:09 PM Β· Difficulty 10.3505 Β· 6,358,682 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
73cadb45ce767c1611e2153e79764e8bcac6a7762cbbad1f5c3cacfcde77d2bc
View on Chainz β†—

Height

#442,458

Difficulty

10.350460

Transactions

1

Size

199 B

Version

2

Bits

0a59b7c5

Nonce

38,538

Timestamp

3/13/2014, 8:28:09 PM

Confirmations

6,358,682

Merkle Root

994a52c7407550c430437476bd076e67cba12464e0ed1e5acd512dab7f776b85
Transactions (1)
Coinbase994a52c7407550…512dab7f776b85
1 in β†’ 1 out9.3200 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.

4.581 Γ— 10⁹²(93-digit number)
45817941155355733370…43670388788566253760
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
4.581 Γ— 10⁹²(93-digit number)
45817941155355733370…43670388788566253759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.581 Γ— 10⁹²(93-digit number)
45817941155355733370…43670388788566253761
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
9.163 Γ— 10⁹²(93-digit number)
91635882310711466741…87340777577132507519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.163 Γ— 10⁹²(93-digit number)
91635882310711466741…87340777577132507521
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
1.832 Γ— 10⁹³(94-digit number)
18327176462142293348…74681555154265015039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.832 Γ— 10⁹³(94-digit number)
18327176462142293348…74681555154265015041
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
3.665 Γ— 10⁹³(94-digit number)
36654352924284586696…49363110308530030079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.665 Γ— 10⁹³(94-digit number)
36654352924284586696…49363110308530030081
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
7.330 Γ— 10⁹³(94-digit number)
73308705848569173392…98726220617060060159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.330 Γ— 10⁹³(94-digit number)
73308705848569173392…98726220617060060161
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 442458

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 73cadb45ce767c1611e2153e79764e8bcac6a7762cbbad1f5c3cacfcde77d2bc

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 #442,458 on Chainz β†—
Circulating Supply:57,653,186 XPMΒ·at block #6,801,139 Β· updates every 60s
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