Home/Chain Registry/Block #2,637,500

Block #2,637,500

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/29/2018, 10:52:50 PM · Difficulty 11.4450 · 4,195,240 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1c4b51f7c1eef342cda5cd67204a92ccb203e10fbd4b5443f597f02b76b27607

View on Chainz ↗

Height

#2,637,500

Difficulty

11.444999

Transactions

Size

426 B

Version

Bits

0b71eb6f

Nonce

421,766,788

Timestamp

4/29/2018, 10:52:50 PM

Confirmations

4,195,240

Merkle Root

be1330ddc17b34473568f0c4d8648a7b3000bd1af696a50a684ac567a42d0203

Transactions (2)

Coinbasee3d3e256bcc8ac…e142490ea3a9af

1 in → 1 out7.6300 XPM110 B

AWcyEdr2…s2sQV8GN

efa09b46acef07…fa8fe28304302b

1 in → 2 out5.3593 XPM227 B

AVhXa3fj…Y6pzurwk AUUyeXNK…nzFxmrbB

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.

7.640 × 10⁹¹(92-digit number)

76401473596597045980…55823553410806283600

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

7.640 × 10⁹¹(92-digit number)

76401473596597045980…55823553410806283599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.640 × 10⁹¹(92-digit number)

76401473596597045980…55823553410806283601

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

1.528 × 10⁹²(93-digit number)

15280294719319409196…11647106821612567199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.528 × 10⁹²(93-digit number)

15280294719319409196…11647106821612567201

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

3.056 × 10⁹²(93-digit number)

30560589438638818392…23294213643225134399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.056 × 10⁹²(93-digit number)

30560589438638818392…23294213643225134401

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

6.112 × 10⁹²(93-digit number)

61121178877277636784…46588427286450268799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.112 × 10⁹²(93-digit number)

61121178877277636784…46588427286450268801

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

1.222 × 10⁹³(94-digit number)

12224235775455527356…93176854572900537599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.222 × 10⁹³(94-digit number)

12224235775455527356…93176854572900537601

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

2.444 × 10⁹³(94-digit number)

24448471550911054713…86353709145801075199

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 2637500

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 1c4b51f7c1eef342cda5cd67204a92ccb203e10fbd4b5443f597f02b76b27607

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 #2,637,500 on Chainz ↗

Block #2,637,500

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