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Block #385,941

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/2/2014, 3:35:33 AM Β· Difficulty 10.4049 Β· 6,439,123 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
aae003bd7b30820e035576abf95cff2ca4edff3e05d871348f9587eded8d0966
View on Chainz β†—

Height

#385,941

Difficulty

10.404868

Transactions

1

Size

207 B

Version

2

Bits

0a67a573

Nonce

66,960

Timestamp

2/2/2014, 3:35:33 AM

Confirmations

6,439,123

Merkle Root

04d4f2955bc16a12620ec0126997914928dc7a0946f566305da9a63b6e28fef7
Transactions (1)
Coinbase04d4f2955bc16a…a9a63b6e28fef7
1 in β†’ 1 out9.2200 XPM116 B
AbwWkWZt…kawDhufa
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.

3.463 Γ— 10⁹⁢(97-digit number)
34631962497985720159…63240752117629681330
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
3.463 Γ— 10⁹⁢(97-digit number)
34631962497985720159…63240752117629681329
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.463 Γ— 10⁹⁢(97-digit number)
34631962497985720159…63240752117629681331
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
6.926 Γ— 10⁹⁢(97-digit number)
69263924995971440319…26481504235259362659
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.926 Γ— 10⁹⁢(97-digit number)
69263924995971440319…26481504235259362661
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
1.385 Γ— 10⁹⁷(98-digit number)
13852784999194288063…52963008470518725319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.385 Γ— 10⁹⁷(98-digit number)
13852784999194288063…52963008470518725321
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
2.770 Γ— 10⁹⁷(98-digit number)
27705569998388576127…05926016941037450639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.770 Γ— 10⁹⁷(98-digit number)
27705569998388576127…05926016941037450641
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
5.541 Γ— 10⁹⁷(98-digit number)
55411139996777152255…11852033882074901279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.541 Γ— 10⁹⁷(98-digit number)
55411139996777152255…11852033882074901281
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 385941

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 aae003bd7b30820e035576abf95cff2ca4edff3e05d871348f9587eded8d0966

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 #385,941 on Chainz β†—
Circulating Supply:57,844,598 XPMΒ·at block #6,825,063 Β· updates every 60s
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