Block #1,534,493

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2016, 6:51:57 AM · Difficulty 10.6175 · 5,277,946 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b87fb954cdc773442a63de01370ca77c977f79b7c442c687d591ac1f26a5afd2

View on Chainz ↗

Height

#1,534,493

Difficulty

10.617501

Transactions

Size

22.44 KB

Version

Bits

0a9e1490

Nonce

149,742,837

Timestamp

4/10/2016, 6:51:57 AM

Confirmations

5,277,946

Mined by

⛏️ P2SHAG7TJUcsHQMijCSAcw891HBXEMuxEGUBHp

Merkle Root

b44e467c2f09694eade11ee0ae1a943a2d055d512feb8d868bae908750014191

Transactions (4)

Coinbased012b527552d7b…ad3205a69f0f80

1 in → 1 out9.1000 XPM110 B

AG7TJUcs…uxEGUBHp

e6f8f98cdd69f6…ca0bf3e1ceffab

51 in → 1 out1122.1713 XPM7.42 KB

AYLfrZe3…AHKJmwdT

0fa49c96c6e8ec…15a3449cd5ff14

51 in → 1 out2757.2641 XPM7.41 KB

AGcmpNtR…ndtA8V9P

984c48a2ef4467…a85dd0371bbe97

51 in → 1 out300.8827 XPM7.42 KB

AYofNiL5…kFNKrCsp

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.

7.971 × 10⁹⁷(98-digit number)

79717535290106129148…72738185539639664639

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

7.971 × 10⁹⁷(98-digit number)

79717535290106129148…72738185539639664639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.971 × 10⁹⁷(98-digit number)

79717535290106129148…72738185539639664641

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

1.594 × 10⁹⁸(99-digit number)

15943507058021225829…45476371079279329279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.594 × 10⁹⁸(99-digit number)

15943507058021225829…45476371079279329281

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

3.188 × 10⁹⁸(99-digit number)

31887014116042451659…90952742158558658559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.188 × 10⁹⁸(99-digit number)

31887014116042451659…90952742158558658561

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

6.377 × 10⁹⁸(99-digit number)

63774028232084903318…81905484317117317119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.377 × 10⁹⁸(99-digit number)

63774028232084903318…81905484317117317121

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

1.275 × 10⁹⁹(100-digit number)

12754805646416980663…63810968634234634239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.275 × 10⁹⁹(100-digit number)

12754805646416980663…63810968634234634241

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 #1,534,493

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