Block #218,724

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/20/2013, 2:43:59 AM · Difficulty 9.9311 · 6,589,439 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c43c134fe2bf9333d82105eada1cbb288affc64ad3ddde2fd16662e550d7feca

View on Chainz ↗

Height

#218,724

Difficulty

9.931053

Transactions

Size

1.11 KB

Version

Bits

09ee5978

Nonce

50,893

Timestamp

10/20/2013, 2:43:59 AM

Confirmations

6,589,439

Mined by

⛏️ P2SHAbuU1HhSi58QcdzhwKqhpJiRG3JPwsJEbB

Merkle Root

25b01d4feab8bbd49801ce4a218924bf7e470bcd2a65c09d4b3a529768133df4

Transactions (3)

Coinbase1b1adce88c53ff…b524de4ee2da38

1 in → 1 out10.1400 XPM110 B

AbuU1HhS…JPwsJEbB

4911dfb0ee944c…af72dab772df59

4 in → 9 out40.5800 XPM773 B

AGdYdg5f…ZrePPako ATqDht7F…xHD53DYv AbuU1HhS…JPwsJEbB APRHg8AF…CAiSnFPk AL7194fk…YNQBVjTB

4885266ee52e2f…e5b499c4fbff41

1 in → 1 out10.1300 XPM159 B

AKtKwNMy…P9Rrrqav

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.

1.693 × 10⁹⁵(96-digit number)

16939440587298860894…90009797137875528959

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

1.693 × 10⁹⁵(96-digit number)

16939440587298860894…90009797137875528959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.693 × 10⁹⁵(96-digit number)

16939440587298860894…90009797137875528961

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

3.387 × 10⁹⁵(96-digit number)

33878881174597721789…80019594275751057919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.387 × 10⁹⁵(96-digit number)

33878881174597721789…80019594275751057921

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

6.775 × 10⁹⁵(96-digit number)

67757762349195443578…60039188551502115839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.775 × 10⁹⁵(96-digit number)

67757762349195443578…60039188551502115841

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

1.355 × 10⁹⁶(97-digit number)

13551552469839088715…20078377103004231679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.355 × 10⁹⁶(97-digit number)

13551552469839088715…20078377103004231681

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

2.710 × 10⁹⁶(97-digit number)

27103104939678177431…40156754206008463359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.710 × 10⁹⁶(97-digit number)

27103104939678177431…40156754206008463361

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.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #218,724

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