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Block #240,274

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/2/2013, 1:22:56 PM Β· Difficulty 9.9561 Β· 6,555,072 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7e099dd694d92d55239d15bd8b6726feba14a5d26407d5a59ce6e57fd01216d7
View on Chainz β†—

Height

#240,274

Difficulty

9.956071

Transactions

1

Size

202 B

Version

2

Bits

09f4c116

Nonce

179,332

Timestamp

11/2/2013, 1:22:56 PM

Confirmations

6,555,072

Merkle Root

56163c93aae903eb268f7151ac00b82f24c701ba264c8cf8bb742873d7b2ea58
Transactions (1)
Coinbase56163c93aae903…742873d7b2ea58
1 in β†’ 1 out10.0700 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.

5.216 Γ— 10⁹⁸(99-digit number)
52162104310813396415…36797431968856253440
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
5.216 Γ— 10⁹⁸(99-digit number)
52162104310813396415…36797431968856253439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.216 Γ— 10⁹⁸(99-digit number)
52162104310813396415…36797431968856253441
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
1.043 Γ— 10⁹⁹(100-digit number)
10432420862162679283…73594863937712506879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.043 Γ— 10⁹⁹(100-digit number)
10432420862162679283…73594863937712506881
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
2.086 Γ— 10⁹⁹(100-digit number)
20864841724325358566…47189727875425013759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.086 Γ— 10⁹⁹(100-digit number)
20864841724325358566…47189727875425013761
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
4.172 Γ— 10⁹⁹(100-digit number)
41729683448650717132…94379455750850027519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.172 Γ— 10⁹⁹(100-digit number)
41729683448650717132…94379455750850027521
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
8.345 Γ— 10⁹⁹(100-digit number)
83459366897301434265…88758911501700055039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.345 Γ— 10⁹⁹(100-digit number)
83459366897301434265…88758911501700055041
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 240274

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 7e099dd694d92d55239d15bd8b6726feba14a5d26407d5a59ce6e57fd01216d7

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 #240,274 on Chainz β†—
Circulating Supply:57,606,821 XPMΒ·at block #6,795,345 Β· updates every 60s
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