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Block #272,287

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/25/2013, 4:21:35 AM Β· Difficulty 9.9526 Β· 6,542,618 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
61ff4cce32eb3a032116f27e09f26e83bd47b8b31b37cfda185f6f22e5ebcb67
View on Chainz β†—

Height

#272,287

Difficulty

9.952572

Transactions

1

Size

208 B

Version

2

Bits

09f3dbbc

Nonce

29,893

Timestamp

11/25/2013, 4:21:35 AM

Confirmations

6,542,618

Merkle Root

05b652d4b8e7bda23ea729b207a6f8a16f7d35bb2f9b6a2cb53e37f0895a1b45
Transactions (1)
Coinbase05b652d4b8e7bd…3e37f0895a1b45
1 in β†’ 1 out10.0800 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.

1.565 Γ— 10⁹⁹(100-digit number)
15652872422220240968…42049125409496695680
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
1.565 Γ— 10⁹⁹(100-digit number)
15652872422220240968…42049125409496695679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.565 Γ— 10⁹⁹(100-digit number)
15652872422220240968…42049125409496695681
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
3.130 Γ— 10⁹⁹(100-digit number)
31305744844440481937…84098250818993391359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.130 Γ— 10⁹⁹(100-digit number)
31305744844440481937…84098250818993391361
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
6.261 Γ— 10⁹⁹(100-digit number)
62611489688880963874…68196501637986782719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.261 Γ— 10⁹⁹(100-digit number)
62611489688880963874…68196501637986782721
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
1.252 Γ— 10¹⁰⁰(101-digit number)
12522297937776192774…36393003275973565439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.252 Γ— 10¹⁰⁰(101-digit number)
12522297937776192774…36393003275973565441
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
2.504 Γ— 10¹⁰⁰(101-digit number)
25044595875552385549…72786006551947130879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.504 Γ— 10¹⁰⁰(101-digit number)
25044595875552385549…72786006551947130881
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 272287

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 61ff4cce32eb3a032116f27e09f26e83bd47b8b31b37cfda185f6f22e5ebcb67

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 #272,287 on Chainz β†—
Circulating Supply:57,763,330 XPMΒ·at block #6,814,904 Β· updates every 60s
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