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Block #226,764

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/25/2013, 11:05:43 AM Β· Difficulty 9.9359 Β· 6,585,614 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
83e0e4dc8ca672988530887c2dee33545d142f610550cddd249ff18aa7b8ae25
View on Chainz β†—

Height

#226,764

Difficulty

9.935884

Transactions

1

Size

797 B

Version

2

Bits

09ef961f

Nonce

55,512

Timestamp

10/25/2013, 11:05:43 AM

Confirmations

6,585,614

Merkle Root

0456c63950d7ecee16ca56290960eae48fbb1cb5a344556be678126f996e5030
Transactions (1)
Coinbase0456c63950d7ec…78126f996e5030
1 in β†’ 19 out10.1100 XPM708 B
AdnG9gQ7…N9B7mA2pAdL4ZZDR…2eQtg1T9AeLjc3ta…6Gk5xuJkAU9KdB9r…o5XC6WMyAabHNb1B…GRoingRy
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.

2.966 Γ— 10⁹³(94-digit number)
29666537466082987027…08035003492114546130
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
2.966 Γ— 10⁹³(94-digit number)
29666537466082987027…08035003492114546129
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.966 Γ— 10⁹³(94-digit number)
29666537466082987027…08035003492114546131
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
5.933 Γ— 10⁹³(94-digit number)
59333074932165974054…16070006984229092259
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.933 Γ— 10⁹³(94-digit number)
59333074932165974054…16070006984229092261
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
1.186 Γ— 10⁹⁴(95-digit number)
11866614986433194810…32140013968458184519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.186 Γ— 10⁹⁴(95-digit number)
11866614986433194810…32140013968458184521
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
2.373 Γ— 10⁹⁴(95-digit number)
23733229972866389621…64280027936916369039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.373 Γ— 10⁹⁴(95-digit number)
23733229972866389621…64280027936916369041
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
4.746 Γ— 10⁹⁴(95-digit number)
47466459945732779243…28560055873832738079
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 226764

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 83e0e4dc8ca672988530887c2dee33545d142f610550cddd249ff18aa7b8ae25

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 #226,764 on Chainz β†—
Circulating Supply:57,743,046 XPMΒ·at block #6,812,377 Β· updates every 60s
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