Block #305,486

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/11/2013, 12:54:46 PM · Difficulty 9.9936 · 6,503,586 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

49effb1a7d8f3d328a29fee3c88c72f0274f9c47565c2200298f33594f2d1d67

View on Chainz ↗

Height

#305,486

Difficulty

9.993594

Transactions

Size

1.05 KB

Version

Bits

09fe5c35

Nonce

186,593

Timestamp

12/11/2013, 12:54:46 PM

Confirmations

6,503,586

Mined by

⛏️ NaR`jAYckRkCFgTH4MEfpDbaimvV5cSTgDe5VSp

Merkle Root

df1fc31744adbc46487c750149b0575de4095d34000d22daf948f223caf7602c

Transactions (1)

Coinbasedf1fc31744adbc…48f223caf7602c

1 in → 27 out10.0000 XPM981 B

AYckRkCF…TgDe5VSp APeshfYV…3PKcKMKH Ad9pSzHt…cpJ3y2zz AQwRN8bE…V8PsTcY9 AY1tyV9E…mJLiTZPS

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.

3.431 × 10⁹⁴(95-digit number)

34316280105636762665…83719939619942756799

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

3.431 × 10⁹⁴(95-digit number)

34316280105636762665…83719939619942756799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.431 × 10⁹⁴(95-digit number)

34316280105636762665…83719939619942756801

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

6.863 × 10⁹⁴(95-digit number)

68632560211273525330…67439879239885513599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.863 × 10⁹⁴(95-digit number)

68632560211273525330…67439879239885513601

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

1.372 × 10⁹⁵(96-digit number)

13726512042254705066…34879758479771027199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.372 × 10⁹⁵(96-digit number)

13726512042254705066…34879758479771027201

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

2.745 × 10⁹⁵(96-digit number)

27453024084509410132…69759516959542054399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.745 × 10⁹⁵(96-digit number)

27453024084509410132…69759516959542054401

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

5.490 × 10⁹⁵(96-digit number)

54906048169018820264…39519033919084108799

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 #305,486

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