Block #319,101

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/18/2013, 7:30:40 PM · Difficulty 10.1646 · 6,486,667 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e7ebf5790ce16e1b6e7a094a4edc6bc90532d5e811fb385bca66c43238f17bed

View on Chainz ↗

Height

#319,101

Difficulty

10.164603

Transactions

Size

1.05 KB

Version

Bits

0a2a2365

Nonce

6,188

Timestamp

12/18/2013, 7:30:40 PM

Confirmations

6,486,667

Mined by

⛏️ }aRAc6mGvmQ9ya8dQxqWNQYGz81U4XqWmPHjR

Merkle Root

f84db3c481dcfe95ca680edae68a01480861a186670ab215146cfc60ec6a2202

Transactions (1)

Coinbasef84db3c481dcfe…6cfc60ec6a2202

1 in → 27 out9.6600 XPM981 B

Ac6mGvmQ…XqWmPHjR AQwRN8bE…V8PsTcY9 Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AHZUHC8g…t3rBwmSA

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.

1.865 × 10¹⁰¹(102-digit number)

18655360967737066075…37767799666071864319

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

1.865 × 10¹⁰¹(102-digit number)

18655360967737066075…37767799666071864319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.865 × 10¹⁰¹(102-digit number)

18655360967737066075…37767799666071864321

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

3.731 × 10¹⁰¹(102-digit number)

37310721935474132150…75535599332143728639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.731 × 10¹⁰¹(102-digit number)

37310721935474132150…75535599332143728641

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

7.462 × 10¹⁰¹(102-digit number)

74621443870948264300…51071198664287457279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.462 × 10¹⁰¹(102-digit number)

74621443870948264300…51071198664287457281

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

1.492 × 10¹⁰²(103-digit number)

14924288774189652860…02142397328574914559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.492 × 10¹⁰²(103-digit number)

14924288774189652860…02142397328574914561

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

2.984 × 10¹⁰²(103-digit number)

29848577548379305720…04284794657149829119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.984 × 10¹⁰²(103-digit number)

29848577548379305720…04284794657149829121

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