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Block #245,063

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/5/2013, 6:21:28 AM Β· Difficulty 9.9634 Β· 6,580,636 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9d2d80bc18d77b3da566003d253fa02feee9cfc0e789b0de5d32413ddaf27568
View on Chainz β†—

Height

#245,063

Difficulty

9.963372

Transactions

1

Size

206 B

Version

2

Bits

09f69f92

Nonce

8,570

Timestamp

11/5/2013, 6:21:28 AM

Confirmations

6,580,636

Merkle Root

9bd3487a9c3d1949e9984339ebc972f958279a8358c43e1e823a9e3fcb90f42f
Transactions (1)
Coinbase9bd3487a9c3d19…3a9e3fcb90f42f
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.

2.152 Γ— 10⁹⁡(96-digit number)
21528057735164853962…49942771718783473000
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
2.152 Γ— 10⁹⁡(96-digit number)
21528057735164853962…49942771718783472999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.152 Γ— 10⁹⁡(96-digit number)
21528057735164853962…49942771718783473001
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
4.305 Γ— 10⁹⁡(96-digit number)
43056115470329707924…99885543437566945999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.305 Γ— 10⁹⁡(96-digit number)
43056115470329707924…99885543437566946001
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
8.611 Γ— 10⁹⁡(96-digit number)
86112230940659415849…99771086875133891999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.611 Γ— 10⁹⁡(96-digit number)
86112230940659415849…99771086875133892001
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
1.722 Γ— 10⁹⁢(97-digit number)
17222446188131883169…99542173750267783999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.722 Γ— 10⁹⁢(97-digit number)
17222446188131883169…99542173750267784001
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
3.444 Γ— 10⁹⁢(97-digit number)
34444892376263766339…99084347500535567999
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 245063

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 9d2d80bc18d77b3da566003d253fa02feee9cfc0e789b0de5d32413ddaf27568

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 #245,063 on Chainz β†—
Circulating Supply:57,849,705 XPMΒ·at block #6,825,698 Β· updates every 60s
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