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Block #2,642,040

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/1/2018, 2:09:03 PM · Difficulty 11.6402 · 4,202,062 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

78f5d5bd3b1413e677723c3d0b9a4d2e588fe3467532ab38f196a6f285ebec76

View on Chainz ↗

Height

#2,642,040

Difficulty

11.640213

Transactions

Size

426 B

Version

Bits

0ba3e503

Nonce

236,434,033

Timestamp

5/1/2018, 2:09:03 PM

Confirmations

4,202,062

Merkle Root

cdfa83bb5978aefaaaac5fad98378835472882ab5641d0dfa868cbbf91fe7f84

Transactions (2)

Coinbaseb60ad0b3a1ae97…32a7c2e680f754

1 in → 1 out7.3800 XPM110 B

ANLwyKdd…am2FfbaK

c50b520793c916…e1715387fe710c

1 in → 2 out19209.2295 XPM226 B

APEPyoow…eSYHVK8t AcMp5yhN…SFpzcvEP

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.

4.667 × 10⁹³(94-digit number)

46675972703782039607…96053425365338768920

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

4.667 × 10⁹³(94-digit number)

46675972703782039607…96053425365338768919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.667 × 10⁹³(94-digit number)

46675972703782039607…96053425365338768921

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

9.335 × 10⁹³(94-digit number)

93351945407564079215…92106850730677537839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.335 × 10⁹³(94-digit number)

93351945407564079215…92106850730677537841

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

1.867 × 10⁹⁴(95-digit number)

18670389081512815843…84213701461355075679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.867 × 10⁹⁴(95-digit number)

18670389081512815843…84213701461355075681

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

3.734 × 10⁹⁴(95-digit number)

37340778163025631686…68427402922710151359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.734 × 10⁹⁴(95-digit number)

37340778163025631686…68427402922710151361

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

7.468 × 10⁹⁴(95-digit number)

74681556326051263372…36854805845420302719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.468 × 10⁹⁴(95-digit number)

74681556326051263372…36854805845420302721

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.493 × 10⁹⁵(96-digit number)

14936311265210252674…73709611690840605439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 2642040

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 78f5d5bd3b1413e677723c3d0b9a4d2e588fe3467532ab38f196a6f285ebec76

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 #2,642,040 on Chainz ↗

Block #2,642,040

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