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Block #398,430

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/10/2014, 5:22:22 PM Β· Difficulty 10.4258 Β· 6,426,147 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ecacdc6faea8d1dce923b408cdec94f215b83df7903857069da6d7a439457e3b
View on Chainz β†—

Height

#398,430

Difficulty

10.425825

Transactions

1

Size

207 B

Version

2

Bits

0a6d02dd

Nonce

892

Timestamp

2/10/2014, 5:22:22 PM

Confirmations

6,426,147

Merkle Root

640824faad7ca3b802e929b619c05ec0352aa7c3c20f3c57d28530d14785dc59
Transactions (1)
Coinbase640824faad7ca3…8530d14785dc59
1 in β†’ 1 out9.1900 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.

3.302 Γ— 10⁹⁢(97-digit number)
33029781596591821304…74519225761604472700
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
3.302 Γ— 10⁹⁢(97-digit number)
33029781596591821304…74519225761604472699
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.302 Γ— 10⁹⁢(97-digit number)
33029781596591821304…74519225761604472701
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
6.605 Γ— 10⁹⁢(97-digit number)
66059563193183642608…49038451523208945399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.605 Γ— 10⁹⁢(97-digit number)
66059563193183642608…49038451523208945401
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
1.321 Γ— 10⁹⁷(98-digit number)
13211912638636728521…98076903046417890799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.321 Γ— 10⁹⁷(98-digit number)
13211912638636728521…98076903046417890801
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
2.642 Γ— 10⁹⁷(98-digit number)
26423825277273457043…96153806092835781599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.642 Γ— 10⁹⁷(98-digit number)
26423825277273457043…96153806092835781601
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
5.284 Γ— 10⁹⁷(98-digit number)
52847650554546914086…92307612185671563199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.284 Γ— 10⁹⁷(98-digit number)
52847650554546914086…92307612185671563201
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 398430

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 ecacdc6faea8d1dce923b408cdec94f215b83df7903857069da6d7a439457e3b

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 #398,430 on Chainz β†—
Circulating Supply:57,840,682 XPMΒ·at block #6,824,576 Β· updates every 60s
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