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Block #399,844

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/11/2014, 4:12:09 PM Β· Difficulty 10.4315 Β· 6,395,929 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7b71e12b9bf877d7118731d59c4fe07eef1a5b13e72bdf096bf52191b97803ee
View on Chainz β†—

Height

#399,844

Difficulty

10.431534

Transactions

2

Size

547 B

Version

2

Bits

0a6e78ff

Nonce

176,511

Timestamp

2/11/2014, 4:12:09 PM

Confirmations

6,395,929

Merkle Root

21e96c244a86f178f98599465582b8cce7bbf5002a4f6801966ff8fdf944aff9
Transactions (2)
Coinbasedf67a53c60f38d…f7ca5b5e43a3b9
1 in β†’ 1 out9.1962 XPM116 B
AbwWkWZt…kawDhufa
b384a501eaa5c6…69e3c4cb221e40
2 in β†’ 1 out1.0000 XPM340 B
Ac8knWXR…uUMyn63E
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— 10⁹⁢(97-digit number)
22807077676445735862…24292162204306238160
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— 10⁹⁢(97-digit number)
22807077676445735862…24292162204306238159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.280 Γ— 10⁹⁢(97-digit number)
22807077676445735862…24292162204306238161
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
4.561 Γ— 10⁹⁢(97-digit number)
45614155352891471725…48584324408612476319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.561 Γ— 10⁹⁢(97-digit number)
45614155352891471725…48584324408612476321
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
9.122 Γ— 10⁹⁢(97-digit number)
91228310705782943450…97168648817224952639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.122 Γ— 10⁹⁢(97-digit number)
91228310705782943450…97168648817224952641
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— 10⁹⁷(98-digit number)
18245662141156588690…94337297634449905279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.824 Γ— 10⁹⁷(98-digit number)
18245662141156588690…94337297634449905281
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
3.649 Γ— 10⁹⁷(98-digit number)
36491324282313177380…88674595268899810559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.649 Γ— 10⁹⁷(98-digit number)
36491324282313177380…88674595268899810561
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 399844

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 7b71e12b9bf877d7118731d59c4fe07eef1a5b13e72bdf096bf52191b97803ee

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 #399,844 on Chainz β†—
Circulating Supply:57,610,267 XPMΒ·at block #6,795,772 Β· updates every 60s
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