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Block #142,774

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/31/2013, 4:33:48 AM Β· Difficulty 9.8379 Β· 6,653,253 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b9f69f9716ac52ea2f118393ca5aebd0f2b16731388a3c49bd010feff2d15763
View on Chainz β†—

Height

#142,774

Difficulty

9.837854

Transactions

1

Size

199 B

Version

2

Bits

09d67d97

Nonce

49,416

Timestamp

8/31/2013, 4:33:48 AM

Confirmations

6,653,253

Merkle Root

20d813a584e0a5a4a921a94183bec0a63c875f4e3ed116fca060746aef9b0d45
Transactions (1)
Coinbase20d813a584e0a5…60746aef9b0d45
1 in β†’ 1 out10.3200 XPM109 B
AUZRUc5X…Yp2sspjk
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.

3.619 Γ— 10⁹⁴(95-digit number)
36195474316464355081…65956443927476467600
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
3.619 Γ— 10⁹⁴(95-digit number)
36195474316464355081…65956443927476467599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.619 Γ— 10⁹⁴(95-digit number)
36195474316464355081…65956443927476467601
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
7.239 Γ— 10⁹⁴(95-digit number)
72390948632928710163…31912887854952935199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.239 Γ— 10⁹⁴(95-digit number)
72390948632928710163…31912887854952935201
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
1.447 Γ— 10⁹⁡(96-digit number)
14478189726585742032…63825775709905870399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.447 Γ— 10⁹⁡(96-digit number)
14478189726585742032…63825775709905870401
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
2.895 Γ— 10⁹⁡(96-digit number)
28956379453171484065…27651551419811740799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.895 Γ— 10⁹⁡(96-digit number)
28956379453171484065…27651551419811740801
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
5.791 Γ— 10⁹⁡(96-digit number)
57912758906342968130…55303102839623481599
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 142774

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 b9f69f9716ac52ea2f118393ca5aebd0f2b16731388a3c49bd010feff2d15763

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 #142,774 on Chainz β†—
Circulating Supply:57,612,308 XPMΒ·at block #6,796,026 Β· updates every 60s
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