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Block #266,155

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/20/2013, 5:01:53 AM Β· Difficulty 9.9611 Β· 6,558,390 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
37d38e08bd7aa768a4a4ecaef380999c006274cf712d864fb4ffefb3fda9cfbb
View on Chainz β†—

Height

#266,155

Difficulty

9.961108

Transactions

1

Size

206 B

Version

2

Bits

09f60b34

Nonce

320,761

Timestamp

11/20/2013, 5:01:53 AM

Confirmations

6,558,390

Merkle Root

2176a492b4fbb5572c311a2d11f7df7614b568908d951ad18575c54fcd549dac
Transactions (1)
Coinbase2176a492b4fbb5…75c54fcd549dac
1 in β†’ 1 out10.0600 XPM116 B
AcLBm5Z9…S683d7c3
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.

5.453 Γ— 10⁹³(94-digit number)
54532147842686800929…40968125496557122560
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
5.453 Γ— 10⁹³(94-digit number)
54532147842686800929…40968125496557122559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.453 Γ— 10⁹³(94-digit number)
54532147842686800929…40968125496557122561
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
1.090 Γ— 10⁹⁴(95-digit number)
10906429568537360185…81936250993114245119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.090 Γ— 10⁹⁴(95-digit number)
10906429568537360185…81936250993114245121
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
2.181 Γ— 10⁹⁴(95-digit number)
21812859137074720371…63872501986228490239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.181 Γ— 10⁹⁴(95-digit number)
21812859137074720371…63872501986228490241
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
4.362 Γ— 10⁹⁴(95-digit number)
43625718274149440743…27745003972456980479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.362 Γ— 10⁹⁴(95-digit number)
43625718274149440743…27745003972456980481
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
8.725 Γ— 10⁹⁴(95-digit number)
87251436548298881487…55490007944913960959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.725 Γ— 10⁹⁴(95-digit number)
87251436548298881487…55490007944913960961
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 266155

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 37d38e08bd7aa768a4a4ecaef380999c006274cf712d864fb4ffefb3fda9cfbb

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 #266,155 on Chainz β†—
Circulating Supply:57,840,422 XPMΒ·at block #6,824,544 Β· updates every 60s
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