Block #337,077

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/31/2013, 10:09:53 AM · Difficulty 10.1397 · 6,468,722 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4ca8e6d9594f4e0fe5664bca60c057c64881cc517d86aa7be0293ce3989ffd1d

View on Chainz ↗

Height

#337,077

Difficulty

10.139725

Transactions

Size

1.01 KB

Version

Bits

0a23c4ff

Nonce

535,769

Timestamp

12/31/2013, 10:09:53 AM

Confirmations

6,468,722

Mined by

⛏️ $aRUAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

877bebd250ed1a666c7251cb4b1aa18de75152c72f5585bc55292b12abebcb10

Transactions (1)

Coinbase877bebd250ed1a…292b12abebcb10

1 in → 26 out9.7100 XPM947 B

Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR AKzkYQaQ…zR4FspJZ AVnJZre9…7fQQrSqU AXz2kWvX…V5ZFCDBd

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.

7.540 × 10⁹⁹(100-digit number)

75407599995056089882…06766531363751512959

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

7.540 × 10⁹⁹(100-digit number)

75407599995056089882…06766531363751512959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.540 × 10⁹⁹(100-digit number)

75407599995056089882…06766531363751512961

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

1.508 × 10¹⁰⁰(101-digit number)

15081519999011217976…13533062727503025919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.508 × 10¹⁰⁰(101-digit number)

15081519999011217976…13533062727503025921

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

3.016 × 10¹⁰⁰(101-digit number)

30163039998022435953…27066125455006051839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.016 × 10¹⁰⁰(101-digit number)

30163039998022435953…27066125455006051841

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

6.032 × 10¹⁰⁰(101-digit number)

60326079996044871906…54132250910012103679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.032 × 10¹⁰⁰(101-digit number)

60326079996044871906…54132250910012103681

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

1.206 × 10¹⁰¹(102-digit number)

12065215999208974381…08264501820024207359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.206 × 10¹⁰¹(102-digit number)

12065215999208974381…08264501820024207361

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