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Block #304,890

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/11/2013, 4:24:18 AM Β· Difficulty 9.9935 Β· 6,522,336 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
080b7c20c26a0c5ba2b7091ebe79d5282cd7db9aa6e2c834c5a9a1e0fdd175ad
View on Chainz β†—

Height

#304,890

Difficulty

9.993471

Transactions

1

Size

199 B

Version

2

Bits

09fe541f

Nonce

876,316

Timestamp

12/11/2013, 4:24:18 AM

Confirmations

6,522,336

Merkle Root

90da815b4e4321a9435a48884ec093912c1acc3032ed260be9a5faf7ee9f92ab
Transactions (1)
Coinbase90da815b4e4321…a5faf7ee9f92ab
1 in β†’ 1 out10.0000 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.

6.822 Γ— 10⁹¹(92-digit number)
68229181867736745296…05924400688887269400
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
6.822 Γ— 10⁹¹(92-digit number)
68229181867736745296…05924400688887269399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.822 Γ— 10⁹¹(92-digit number)
68229181867736745296…05924400688887269401
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
1.364 Γ— 10⁹²(93-digit number)
13645836373547349059…11848801377774538799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.364 Γ— 10⁹²(93-digit number)
13645836373547349059…11848801377774538801
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
2.729 Γ— 10⁹²(93-digit number)
27291672747094698118…23697602755549077599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.729 Γ— 10⁹²(93-digit number)
27291672747094698118…23697602755549077601
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
5.458 Γ— 10⁹²(93-digit number)
54583345494189396237…47395205511098155199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.458 Γ— 10⁹²(93-digit number)
54583345494189396237…47395205511098155201
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
1.091 Γ— 10⁹³(94-digit number)
10916669098837879247…94790411022196310399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.091 Γ— 10⁹³(94-digit number)
10916669098837879247…94790411022196310401
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 304890

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 080b7c20c26a0c5ba2b7091ebe79d5282cd7db9aa6e2c834c5a9a1e0fdd175ad

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 #304,890 on Chainz β†—
Circulating Supply:57,861,907 XPMΒ·at block #6,827,225 Β· updates every 60s
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