Block #523,359

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/3/2014, 1:27:14 PM · Difficulty 10.8718 · 6,286,224 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

82b7d017ea3a9a585d61c35737e0399e775897c865cd1e9446e6b9ab53f70f27

View on Chainz ↗

Height

#523,359

Difficulty

10.871777

Transactions

Size

436 B

Version

Bits

0adf2cc2

Nonce

25,033,315

Timestamp

5/3/2014, 1:27:14 PM

Confirmations

6,286,224

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

a1578cb76b96c34e0dbe34ef752ee895a5f53219f9f91f945e832c46d6c46619

Transactions (2)

Coinbase1a05a0ab0662ad…465caac15aef7c

1 in → 1 out8.4600 XPM116 B

AbwWkWZt…kawDhufa

2ad1a8ffa53302…27d1564607b747

1 in → 2 out8.4600 XPM227 B

AVunGX29…zD9xLjm3 ATsNuVSo…9WTtpT6v

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.

9.248 × 10¹⁰⁰(101-digit number)

92486674118030901066…65309249166191493119

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

9.248 × 10¹⁰⁰(101-digit number)

92486674118030901066…65309249166191493119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.248 × 10¹⁰⁰(101-digit number)

92486674118030901066…65309249166191493121

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

1.849 × 10¹⁰¹(102-digit number)

18497334823606180213…30618498332382986239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.849 × 10¹⁰¹(102-digit number)

18497334823606180213…30618498332382986241

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

3.699 × 10¹⁰¹(102-digit number)

36994669647212360426…61236996664765972479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.699 × 10¹⁰¹(102-digit number)

36994669647212360426…61236996664765972481

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

7.398 × 10¹⁰¹(102-digit number)

73989339294424720853…22473993329531944959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.398 × 10¹⁰¹(102-digit number)

73989339294424720853…22473993329531944961

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

1.479 × 10¹⁰²(103-digit number)

14797867858884944170…44947986659063889919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.479 × 10¹⁰²(103-digit number)

14797867858884944170…44947986659063889921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.959 × 10¹⁰²(103-digit number)

29595735717769888341…89895973318127779839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #523,359

Cookie Preferences