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Block #380,596

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/29/2014, 9:16:26 AM Β· Difficulty 10.4117 Β· 6,420,394 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b58e864c27b9beef45d5a720decfa6308a8a6e3fc070612790b79ec21736e9e9
View on Chainz β†—

Height

#380,596

Difficulty

10.411671

Transactions

1

Size

201 B

Version

2

Bits

0a69633e

Nonce

230,347

Timestamp

1/29/2014, 9:16:26 AM

Confirmations

6,420,394

Merkle Root

12fdb07883424fd0ade7ff8b8ac6cc1fbec0fd65bbe302d4d0d0e3f4b3f52f87
Transactions (1)
Coinbase12fdb07883424f…d0e3f4b3f52f87
1 in β†’ 1 out9.2100 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.

3.753 Γ— 10⁹⁢(97-digit number)
37532182511661327476…61864673511531382200
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
3.753 Γ— 10⁹⁢(97-digit number)
37532182511661327476…61864673511531382199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.753 Γ— 10⁹⁢(97-digit number)
37532182511661327476…61864673511531382201
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
7.506 Γ— 10⁹⁢(97-digit number)
75064365023322654953…23729347023062764399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.506 Γ— 10⁹⁢(97-digit number)
75064365023322654953…23729347023062764401
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
1.501 Γ— 10⁹⁷(98-digit number)
15012873004664530990…47458694046125528799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.501 Γ— 10⁹⁷(98-digit number)
15012873004664530990…47458694046125528801
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
3.002 Γ— 10⁹⁷(98-digit number)
30025746009329061981…94917388092251057599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.002 Γ— 10⁹⁷(98-digit number)
30025746009329061981…94917388092251057601
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
6.005 Γ— 10⁹⁷(98-digit number)
60051492018658123962…89834776184502115199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.005 Γ— 10⁹⁷(98-digit number)
60051492018658123962…89834776184502115201
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 380596

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 b58e864c27b9beef45d5a720decfa6308a8a6e3fc070612790b79ec21736e9e9

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 #380,596 on Chainz β†—
Circulating Supply:57,651,980 XPMΒ·at block #6,800,989 Β· updates every 60s
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