Block #307,366

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/12/2013, 1:11:00 PM · Difficulty 9.9942 · 6,508,477 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

11046d20931c71dee12859bff715c224063e0a28e14e7c060b6a30cd7f3afd8b

View on Chainz ↗

Height

#307,366

Difficulty

9.994177

Transactions

Size

1.11 KB

Version

Bits

09fe825c

Nonce

330,823

Timestamp

12/12/2013, 1:11:00 PM

Confirmations

6,508,477

Mined by

⛏️ aRI~APeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

b9f4f59dc14c09f603619314dc8ff0f744cfc2d43cbc8e84c4116ebd081f388f

Transactions (1)

Coinbaseb9f4f59dc14c09…116ebd081f388f

1 in → 29 out9.9800 XPM1.02 KB

APeshfYV…3PKcKMKH Ad9pSzHt…cpJ3y2zz Aac9Hjdg…P4ktypc3 ALnB8QRd…ZpnGtr1t AFpbuSgY…J2xyG5Rg

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.

5.118 × 10⁹⁵(96-digit number)

51180269261207258078…33411985918878835839

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

5.118 × 10⁹⁵(96-digit number)

51180269261207258078…33411985918878835839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.118 × 10⁹⁵(96-digit number)

51180269261207258078…33411985918878835841

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

1.023 × 10⁹⁶(97-digit number)

10236053852241451615…66823971837757671679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.023 × 10⁹⁶(97-digit number)

10236053852241451615…66823971837757671681

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

2.047 × 10⁹⁶(97-digit number)

20472107704482903231…33647943675515343359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.047 × 10⁹⁶(97-digit number)

20472107704482903231…33647943675515343361

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

4.094 × 10⁹⁶(97-digit number)

40944215408965806462…67295887351030686719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.094 × 10⁹⁶(97-digit number)

40944215408965806462…67295887351030686721

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

8.188 × 10⁹⁶(97-digit number)

81888430817931612925…34591774702061373439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.188 × 10⁹⁶(97-digit number)

81888430817931612925…34591774702061373441

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 #307,366

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