Block #218,582

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/20/2013, 12:47:46 AM · Difficulty 9.9308 · 6,592,410 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

836ff69c2b2eb197281236356d75a9ae92d2b3cef3e11e9438d79217ee5e07c3

View on Chainz ↗

Height

#218,582

Difficulty

9.930752

Transactions

Size

1.44 KB

Version

Bits

09ee45c0

Nonce

61,896

Timestamp

10/20/2013, 12:47:46 AM

Confirmations

6,592,410

Mined by

⛏️ URc'AFqKfjezAQpHxUWGcDetimH5AUqX9Ace3g

Merkle Root

a06f12ac779468044568271262e60f4a24a7240b26e1616f3c4c4e1d2bdccda0

Transactions (1)

Coinbasea06f12ac779468…4c4e1d2bdccda0

1 in → 39 out10.1000 XPM1.36 KB

AFqKfjez…qX9Ace3g AbeUZSvK…ijGzuyjz AUT1qxTx…t5B3qd8Z AKFBsJ1Y…LYyU7TbU AXpmXsTH…1zkdde3r

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.

3.962 × 10⁹²(93-digit number)

39626075468630010303…02623160864710329599

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

3.962 × 10⁹²(93-digit number)

39626075468630010303…02623160864710329599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.962 × 10⁹²(93-digit number)

39626075468630010303…02623160864710329601

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

7.925 × 10⁹²(93-digit number)

79252150937260020607…05246321729420659199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.925 × 10⁹²(93-digit number)

79252150937260020607…05246321729420659201

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

1.585 × 10⁹³(94-digit number)

15850430187452004121…10492643458841318399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.585 × 10⁹³(94-digit number)

15850430187452004121…10492643458841318401

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

3.170 × 10⁹³(94-digit number)

31700860374904008243…20985286917682636799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.170 × 10⁹³(94-digit number)

31700860374904008243…20985286917682636801

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

6.340 × 10⁹³(94-digit number)

63401720749808016486…41970573835365273599

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.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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

Cross-reference on Chainz Explorer

Block #218,582

Cookie Preferences