Home/Chain Registry/Block #124,425

Block #124,425

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/19/2013, 3:45:32 PM · Difficulty 9.7701 · 6,692,264 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

96018613c19eb4e65a4601766878d934b3c2b147a13b7e16fc3601125a52e664

View on Chainz ↗

Height

#124,425

Difficulty

9.770145

Transactions

Size

206 B

Version

Bits

09c52841

Nonce

15,809

Timestamp

8/19/2013, 3:45:32 PM

Confirmations

6,692,264

Merkle Root

56a991531fb870f5fcea0d0895ba962583ff82783a6b6fa19cad1bdb9aec9bda

Transactions (1)

Coinbase56a991531fb870…ad1bdb9aec9bda

1 in → 1 out10.4600 XPM109 B

AXEBNNcS…4FopSeij

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.909 × 10¹¹¹(112-digit number)

29095315331224944493…01768536857022943080

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

2.909 × 10¹¹¹(112-digit number)

29095315331224944493…01768536857022943079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.909 × 10¹¹¹(112-digit number)

29095315331224944493…01768536857022943081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

5.819 × 10¹¹¹(112-digit number)

58190630662449888986…03537073714045886159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.819 × 10¹¹¹(112-digit number)

58190630662449888986…03537073714045886161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.163 × 10¹¹²(113-digit number)

11638126132489977797…07074147428091772319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.163 × 10¹¹²(113-digit number)

11638126132489977797…07074147428091772321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.327 × 10¹¹²(113-digit number)

23276252264979955594…14148294856183544639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.327 × 10¹¹²(113-digit number)

23276252264979955594…14148294856183544641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

4.655 × 10¹¹²(113-digit number)

46552504529959911189…28296589712367089279

Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — 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 →

★☆☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 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 124425

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 96018613c19eb4e65a4601766878d934b3c2b147a13b7e16fc3601125a52e664

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 → Debug Window → 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 #124,425 on Chainz ↗

Block #124,425

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