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Block #43,026

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 7:58:43 PM Β· Difficulty 8.6391 Β· 6,751,693 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0012d9ca7d931b515c53eb230fbd5f8fe5fc9d0ce7dbad859440c0784eafb3aa
View on Chainz β†—

Height

#43,026

Difficulty

8.639073

Transactions

1

Size

201 B

Version

2

Bits

08a39a51

Nonce

956

Timestamp

7/14/2013, 7:58:43 PM

Confirmations

6,751,693

Merkle Root

d99768d2de580f1b6c9e92df4f4dc7eece984bcd08f0014661b191b0a7d72b8f
Transactions (1)
Coinbased99768d2de580f…b191b0a7d72b8f
1 in β†’ 1 out13.3800 XPM110 B
AN1jcsfg…JoSA7ph8
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.

5.194 Γ— 10⁹⁢(97-digit number)
51940302483104761136…85052888407539125600
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
5.194 Γ— 10⁹⁢(97-digit number)
51940302483104761136…85052888407539125599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.194 Γ— 10⁹⁢(97-digit number)
51940302483104761136…85052888407539125601
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
1.038 Γ— 10⁹⁷(98-digit number)
10388060496620952227…70105776815078251199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.038 Γ— 10⁹⁷(98-digit number)
10388060496620952227…70105776815078251201
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
2.077 Γ— 10⁹⁷(98-digit number)
20776120993241904454…40211553630156502399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.077 Γ— 10⁹⁷(98-digit number)
20776120993241904454…40211553630156502401
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
4.155 Γ— 10⁹⁷(98-digit number)
41552241986483808909…80423107260313004799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.155 Γ— 10⁹⁷(98-digit number)
41552241986483808909…80423107260313004801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8
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 43026

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 0012d9ca7d931b515c53eb230fbd5f8fe5fc9d0ce7dbad859440c0784eafb3aa

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 #43,026 on Chainz β†—
Circulating Supply:57,601,801 XPMΒ·at block #6,794,718 Β· updates every 60s
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