Block #1,773,304

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/21/2016, 5:31:36 PM · Difficulty 10.7509 · 5,043,372 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

424fe6b19d8e5c59981b5105492d16e219f2e04023395a04eba8e76309611120

View on Chainz ↗

Height

#1,773,304

Difficulty

10.750861

Transactions

Size

3.89 KB

Version

Bits

0ac0386e

Nonce

41,490,332

Timestamp

9/21/2016, 5:31:36 PM

Confirmations

5,043,372

Mined by

⛏️ P2SHATchrxV5AicrjVFZfT7THhZZShSZcmPR98

Merkle Root

d8ac585686713b40f279050f8dbfcdda88a6c2572324db801d37ec7f1b547864

Transactions (3)

Coinbase7e7c9410e8a88a…fb084ab7b78876

1 in → 1 out8.6800 XPM110 B

ATchrxV5…SZcmPR98

66cb0053775f7e…29b14a3b23f6dd

1 in → 51 out143.4437 XPM1.85 KB

Adn7kcGt…hQNStFPQ AbQb3hJU…AKcHCX3s AJ5u3Hok…zj9uSzXD AUKMiWwK…QYx9bxGV AVbiKTS8…94szuneW

61d9fcef87a4ad…e9b9417cc28384

1 in → 51 out7.4389 XPM1.85 KB

AP8WCqkN…VGDK22ag AHVGbgNY…xDDUahUQ AeWrUyu9…KHYAiwxy Aavs1RKL…KhWZvgVb ALVG5rsB…PT83RdE9

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.

8.132 × 10⁹⁴(95-digit number)

81320428084683443983…68592698709614876959

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

8.132 × 10⁹⁴(95-digit number)

81320428084683443983…68592698709614876959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.132 × 10⁹⁴(95-digit number)

81320428084683443983…68592698709614876961

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

1.626 × 10⁹⁵(96-digit number)

16264085616936688796…37185397419229753919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.626 × 10⁹⁵(96-digit number)

16264085616936688796…37185397419229753921

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

3.252 × 10⁹⁵(96-digit number)

32528171233873377593…74370794838459507839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.252 × 10⁹⁵(96-digit number)

32528171233873377593…74370794838459507841

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

6.505 × 10⁹⁵(96-digit number)

65056342467746755187…48741589676919015679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.505 × 10⁹⁵(96-digit number)

65056342467746755187…48741589676919015681

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

1.301 × 10⁹⁶(97-digit number)

13011268493549351037…97483179353838031359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.301 × 10⁹⁶(97-digit number)

13011268493549351037…97483179353838031361

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 #1,773,304

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