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Block #403,073

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/13/2014, 9:40:08 PM Β· Difficulty 10.4350 Β· 6,422,324 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
35e90a30bcf9fbba5d83e73ad06db98e0ed6044a22174b9580451a21a3855ac9
View on Chainz β†—

Height

#403,073

Difficulty

10.435050

Transactions

2

Size

2.73 KB

Version

2

Bits

0a6f5f6f

Nonce

260,944

Timestamp

2/13/2014, 9:40:08 PM

Confirmations

6,422,324

Merkle Root

4bfad4ca2246b474e2412ea21a0e9b68182641b0eccd916e18908c99e69cf2a6
Transactions (2)
Coinbase31267860f050a0…2d818904eb74be
1 in β†’ 1 out9.2000 XPM110 B
AeKNrjNj…1NEq95Ta
7f023ebe6eb63f…ba4c3b7aede462
17 in β†’ 2 out339.5370 XPM2.53 KB
Ac7RAQMV…nKWU2GLUAGasuqcM…P1XTB7qG
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.

5.338 Γ— 10⁹³(94-digit number)
53385890932594117006…67300744302955575500
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
5.338 Γ— 10⁹³(94-digit number)
53385890932594117006…67300744302955575499
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.338 Γ— 10⁹³(94-digit number)
53385890932594117006…67300744302955575501
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
1.067 Γ— 10⁹⁴(95-digit number)
10677178186518823401…34601488605911150999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.067 Γ— 10⁹⁴(95-digit number)
10677178186518823401…34601488605911151001
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
2.135 Γ— 10⁹⁴(95-digit number)
21354356373037646802…69202977211822301999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.135 Γ— 10⁹⁴(95-digit number)
21354356373037646802…69202977211822302001
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
4.270 Γ— 10⁹⁴(95-digit number)
42708712746075293604…38405954423644603999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.270 Γ— 10⁹⁴(95-digit number)
42708712746075293604…38405954423644604001
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
8.541 Γ— 10⁹⁴(95-digit number)
85417425492150587209…76811908847289207999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.541 Γ— 10⁹⁴(95-digit number)
85417425492150587209…76811908847289208001
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 403073

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 35e90a30bcf9fbba5d83e73ad06db98e0ed6044a22174b9580451a21a3855ac9

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 #403,073 on Chainz β†—
Circulating Supply:57,847,276 XPMΒ·at block #6,825,396 Β· updates every 60s
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