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Block #2,057,423

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2017, 8:28:39 PM · Difficulty 10.8310 · 4,787,007 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

60c11b65bdc6f9e1ff3123a4aef915b1a550520bcc31e7c3fd62a38c19aa58c9

View on Chainz ↗

Height

#2,057,423

Difficulty

10.831030

Transactions

Size

426 B

Version

Bits

0ad4be5d

Nonce

759,586,381

Timestamp

4/5/2017, 8:28:39 PM

Confirmations

4,787,007

Merkle Root

c6aa22ba3a67f76306eb13b5dbfb507df0b20745df8098ab5e37a005f16089cf

Transactions (2)

Coinbaseb2bfc3902c7851…f1e2e13f374f98

1 in → 1 out8.5200 XPM109 B

AUAw7QNs…EB9RA4vG

a7aea34f617966…1c9eb897c11614

1 in → 2 out30.6366 XPM225 B

AN83v1TU…kcXerDsJ AXTxiKBB…nskkm6Yv

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.

2.351 × 10⁹⁸(99-digit number)

23512287050446062793…37134187704620974080

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

2.351 × 10⁹⁸(99-digit number)

23512287050446062793…37134187704620974079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.351 × 10⁹⁸(99-digit number)

23512287050446062793…37134187704620974081

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

4.702 × 10⁹⁸(99-digit number)

47024574100892125586…74268375409241948159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.702 × 10⁹⁸(99-digit number)

47024574100892125586…74268375409241948161

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

9.404 × 10⁹⁸(99-digit number)

94049148201784251173…48536750818483896319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.404 × 10⁹⁸(99-digit number)

94049148201784251173…48536750818483896321

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

1.880 × 10⁹⁹(100-digit number)

18809829640356850234…97073501636967792639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.880 × 10⁹⁹(100-digit number)

18809829640356850234…97073501636967792641

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

3.761 × 10⁹⁹(100-digit number)

37619659280713700469…94147003273935585279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.761 × 10⁹⁹(100-digit number)

37619659280713700469…94147003273935585281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

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 — 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

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 × 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 2057423

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 60c11b65bdc6f9e1ff3123a4aef915b1a550520bcc31e7c3fd62a38c19aa58c9

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 #2,057,423 on Chainz ↗

Block #2,057,423

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