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Block #442,838

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/14/2014, 3:37:15 AM Β· Difficulty 10.3430 Β· 6,383,660 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d7bfc0db71ff31ca9359a820f83b4883b4a749cea9da1c3362ecd55d9f3a4918
View on Chainz β†—

Height

#442,838

Difficulty

10.342989

Transactions

1

Size

202 B

Version

2

Bits

0a57ce28

Nonce

350,615

Timestamp

3/14/2014, 3:37:15 AM

Confirmations

6,383,660

Merkle Root

a68846a1921f50916ae30e720baa34b829d2a017ec7c464ba58d780d2d83d7c2
Transactions (1)
Coinbasea68846a1921f50…8d780d2d83d7c2
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.

2.280 Γ— 10¹⁰⁰(101-digit number)
22800830886297495487…80842584533182184960
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
2.280 Γ— 10¹⁰⁰(101-digit number)
22800830886297495487…80842584533182184959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.280 Γ— 10¹⁰⁰(101-digit number)
22800830886297495487…80842584533182184961
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
4.560 Γ— 10¹⁰⁰(101-digit number)
45601661772594990975…61685169066364369919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.560 Γ— 10¹⁰⁰(101-digit number)
45601661772594990975…61685169066364369921
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
9.120 Γ— 10¹⁰⁰(101-digit number)
91203323545189981950…23370338132728739839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.120 Γ— 10¹⁰⁰(101-digit number)
91203323545189981950…23370338132728739841
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
1.824 Γ— 10¹⁰¹(102-digit number)
18240664709037996390…46740676265457479679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.824 Γ— 10¹⁰¹(102-digit number)
18240664709037996390…46740676265457479681
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
3.648 Γ— 10¹⁰¹(102-digit number)
36481329418075992780…93481352530914959359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.648 Γ— 10¹⁰¹(102-digit number)
36481329418075992780…93481352530914959361
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 442838

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 d7bfc0db71ff31ca9359a820f83b4883b4a749cea9da1c3362ecd55d9f3a4918

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 #442,838 on Chainz β†—
Circulating Supply:57,856,126 XPMΒ·at block #6,826,497 Β· updates every 60s
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