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Block #244,804

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/5/2013, 2:30:36 AM Β· Difficulty 9.9632 Β· 6,589,054 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c657fd250081e9735fb99b4df74cc7dd528f9a49efdb32973830862a55b2ad4b
View on Chainz β†—

Height

#244,804

Difficulty

9.963162

Transactions

1

Size

199 B

Version

2

Bits

09f691c2

Nonce

123,592

Timestamp

11/5/2013, 2:30:36 AM

Confirmations

6,589,054

Merkle Root

ba24829a6a24a67de8da8971dd14618f3dc900170e313e29f1d08483801c9b0d
Transactions (1)
Coinbaseba24829a6a24a6…d08483801c9b0d
1 in β†’ 1 out10.0600 XPM109 B
AehGCoKr…7reJxtvk
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.

2.216 Γ— 10⁹⁴(95-digit number)
22161567709298837334…46692781882246132200
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
2.216 Γ— 10⁹⁴(95-digit number)
22161567709298837334…46692781882246132199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.216 Γ— 10⁹⁴(95-digit number)
22161567709298837334…46692781882246132201
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
4.432 Γ— 10⁹⁴(95-digit number)
44323135418597674668…93385563764492264399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.432 Γ— 10⁹⁴(95-digit number)
44323135418597674668…93385563764492264401
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
8.864 Γ— 10⁹⁴(95-digit number)
88646270837195349337…86771127528984528799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.864 Γ— 10⁹⁴(95-digit number)
88646270837195349337…86771127528984528801
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
1.772 Γ— 10⁹⁡(96-digit number)
17729254167439069867…73542255057969057599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.772 Γ— 10⁹⁡(96-digit number)
17729254167439069867…73542255057969057601
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
3.545 Γ— 10⁹⁡(96-digit number)
35458508334878139735…47084510115938115199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.545 Γ— 10⁹⁡(96-digit number)
35458508334878139735…47084510115938115201
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 244804

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 c657fd250081e9735fb99b4df74cc7dd528f9a49efdb32973830862a55b2ad4b

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 #244,804 on Chainz β†—
Circulating Supply:57,915,093 XPMΒ·at block #6,833,857 Β· updates every 60s
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