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Block #266,294

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/20/2013, 7:54:36 AM Β· Difficulty 9.9609 Β· 6,560,596 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cb8aff9f93e309a71b0a7088b3cd821fa3b86debd245d7467e5e01f56abc92f9
View on Chainz β†—

Height

#266,294

Difficulty

9.960899

Transactions

1

Size

187 B

Version

2

Bits

09f5fd80

Nonce

85,030

Timestamp

11/20/2013, 7:54:36 AM

Confirmations

6,560,596

Merkle Root

0947d64ec9b592ca66ed933534a9239015529a8773b854723fc770df50c52405
Transactions (1)
Coinbase0947d64ec9b592…c770df50c52405
1 in β†’ 1 out10.0600 XPM97 B
ALFhmsQi…V5bffJmU
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.

3.032 Γ— 10⁹⁴(95-digit number)
30326543088881625135…17398399301403427840
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
3.032 Γ— 10⁹⁴(95-digit number)
30326543088881625135…17398399301403427839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.032 Γ— 10⁹⁴(95-digit number)
30326543088881625135…17398399301403427841
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
6.065 Γ— 10⁹⁴(95-digit number)
60653086177763250271…34796798602806855679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.065 Γ— 10⁹⁴(95-digit number)
60653086177763250271…34796798602806855681
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
1.213 Γ— 10⁹⁡(96-digit number)
12130617235552650054…69593597205613711359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.213 Γ— 10⁹⁡(96-digit number)
12130617235552650054…69593597205613711361
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
2.426 Γ— 10⁹⁡(96-digit number)
24261234471105300108…39187194411227422719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.426 Γ— 10⁹⁡(96-digit number)
24261234471105300108…39187194411227422721
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
4.852 Γ— 10⁹⁡(96-digit number)
48522468942210600217…78374388822454845439
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 266294

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 cb8aff9f93e309a71b0a7088b3cd821fa3b86debd245d7467e5e01f56abc92f9

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 #266,294 on Chainz β†—
Circulating Supply:57,859,285 XPMΒ·at block #6,826,889 Β· updates every 60s
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