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Block #249,242

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/7/2013, 8:25:36 PM Β· Difficulty 9.9667 Β· 6,575,225 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b810fa981524dc7e806ba08896b3f453d80391958043b98284b021068dc6b6b2
View on Chainz β†—

Height

#249,242

Difficulty

9.966701

Transactions

1

Size

200 B

Version

2

Bits

09f779b4

Nonce

46,139

Timestamp

11/7/2013, 8:25:36 PM

Confirmations

6,575,225

Merkle Root

54c364a93945e500513bbfc2ef357ebb01c36fcdf3add1fa8ec0a06138d34c3d
Transactions (1)
Coinbase54c364a93945e5…c0a06138d34c3d
1 in β†’ 1 out10.0500 XPM109 B
ARAnHftR…VdfpqbzP
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.

5.097 Γ— 10⁹⁷(98-digit number)
50971516396606251189…40725803095230551040
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
5.097 Γ— 10⁹⁷(98-digit number)
50971516396606251189…40725803095230551039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.097 Γ— 10⁹⁷(98-digit number)
50971516396606251189…40725803095230551041
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
1.019 Γ— 10⁹⁸(99-digit number)
10194303279321250237…81451606190461102079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.019 Γ— 10⁹⁸(99-digit number)
10194303279321250237…81451606190461102081
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
2.038 Γ— 10⁹⁸(99-digit number)
20388606558642500475…62903212380922204159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.038 Γ— 10⁹⁸(99-digit number)
20388606558642500475…62903212380922204161
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
4.077 Γ— 10⁹⁸(99-digit number)
40777213117285000951…25806424761844408319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.077 Γ— 10⁹⁸(99-digit number)
40777213117285000951…25806424761844408321
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
8.155 Γ— 10⁹⁸(99-digit number)
81554426234570001903…51612849523688816639
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 249242

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 b810fa981524dc7e806ba08896b3f453d80391958043b98284b021068dc6b6b2

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 #249,242 on Chainz β†—
Circulating Supply:57,839,805 XPMΒ·at block #6,824,466 Β· updates every 60s
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