Block #218,454

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/19/2013, 10:43:25 PM · Difficulty 9.9306 · 6,590,964 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

666b9ce02b5ba3158e6ba3ebc800845c612420ab16fa0368876f7a1b8074b9f6

View on Chainz ↗

Height

#218,454

Difficulty

9.930597

Transactions

Size

2.01 KB

Version

Bits

09ee3b9f

Nonce

7,874

Timestamp

10/19/2013, 10:43:25 PM

Confirmations

6,590,964

Mined by

⛏️ P2SHAVXA3Fnhcnyh7bPQChQcUJsiAXxtjJF2gb

Merkle Root

2d356656c1e47e8691d87e6e03cc0b9d9c3f4ae9decd14be8edc98b7ae740279

Transactions (5)

Coinbase3fb7d4cb8eff79…5eac92dcf38012

1 in → 1 out10.1785 XPM109 B

AVXA3Fnh…xtjJF2gb

d5ac6f14099bbf…334da88571119f

4 in → 8 out38.7703 XPM773 B

AaEoqAqJ…dmRpi31P Abu1uzTT…6jPtvXzW ALsqSwWV…uZ7sTz8x AdToHhys…uNu3dqWo APd3tden…qhRE2ARG

d66e474eea01cc…52234b949537a4

3 in → 2 out20.9357 XPM524 B

AcuM7XiJ…5uND8Jce AeXGzceo…PeqnaR3s

87746683b2c677…420a3c72616aab

2 in → 1 out3.9900 XPM341 B

AVKZm1ay…XpHNs2Bd

e42dfd74ce2287…4c59d9f67b8dde

1 in → 2 out5.0614 XPM227 B

Ab3dSvM7…Qoxxb9tp ASmX9j3e…RJSqaMKm

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.

2.078 × 10⁹³(94-digit number)

20781228716402444825…53207449262997070219

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

2.078 × 10⁹³(94-digit number)

20781228716402444825…53207449262997070219

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.078 × 10⁹³(94-digit number)

20781228716402444825…53207449262997070221

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

4.156 × 10⁹³(94-digit number)

41562457432804889651…06414898525994140439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.156 × 10⁹³(94-digit number)

41562457432804889651…06414898525994140441

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

8.312 × 10⁹³(94-digit number)

83124914865609779302…12829797051988280879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.312 × 10⁹³(94-digit number)

83124914865609779302…12829797051988280881

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

1.662 × 10⁹⁴(95-digit number)

16624982973121955860…25659594103976561759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.662 × 10⁹⁴(95-digit number)

16624982973121955860…25659594103976561761

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

3.324 × 10⁹⁴(95-digit number)

33249965946243911721…51319188207953123519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.324 × 10⁹⁴(95-digit number)

33249965946243911721…51319188207953123521

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 #218,454

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