Block #342,554

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/4/2014, 3:46:07 AM · Difficulty 10.1582 · 6,466,196 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

06930d80324ad3aea2552aaff3533f64c147dcc1e6528a5ae368a47a17382bc8

View on Chainz ↗

Height

#342,554

Difficulty

10.158225

Transactions

Size

2.06 KB

Version

Bits

0a288170

Nonce

25,132

Timestamp

1/4/2014, 3:46:07 AM

Confirmations

6,466,196

Mined by

⛏️ :aRAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

3e87f65dca7e4199f5fd7263760aeff55d94f19ddfed4e01430822f82b37933c

Transactions (2)

Coinbasefb912685aff575…7f425f0af72e38

1 in → 29 out9.6600 XPM1.02 KB

AQwRN8bE…V8PsTcY9 AYtDvcGs…VuAcA7m7 AFutDVqJ…TJTJj6UF AbJY5neX…1Qu8eT6s AYRNBPg5…3q2SvNy5

b258b5738f3bce…577844cc61d85b

6 in → 2 out29.5059 XPM965 B

AWUFK6Gk…dPt2Sp7R AUt7yYNV…Na15R1XU

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.

6.137 × 10¹⁰³(104-digit number)

61373085878450776152…72625225030129827839

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

6.137 × 10¹⁰³(104-digit number)

61373085878450776152…72625225030129827839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.137 × 10¹⁰³(104-digit number)

61373085878450776152…72625225030129827841

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

1.227 × 10¹⁰⁴(105-digit number)

12274617175690155230…45250450060259655679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.227 × 10¹⁰⁴(105-digit number)

12274617175690155230…45250450060259655681

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

2.454 × 10¹⁰⁴(105-digit number)

24549234351380310460…90500900120519311359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.454 × 10¹⁰⁴(105-digit number)

24549234351380310460…90500900120519311361

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

4.909 × 10¹⁰⁴(105-digit number)

49098468702760620921…81001800241038622719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.909 × 10¹⁰⁴(105-digit number)

49098468702760620921…81001800241038622721

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

9.819 × 10¹⁰⁴(105-digit number)

98196937405521241843…62003600482077245439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.819 × 10¹⁰⁴(105-digit number)

98196937405521241843…62003600482077245441

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 #342,554

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