Block #370,204

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/21/2014, 10:29:43 PM · Difficulty 10.4468 · 6,456,410 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d7cd0e27303f89a3e0d0c90b4d6cecf523174567caf8d9d4db516779309a6db1

View on Chainz ↗

Height

#370,204

Difficulty

10.446805

Transactions

Size

397 B

Version

Bits

0a7261cf

Nonce

3,770

Timestamp

1/21/2014, 10:29:43 PM

Confirmations

6,456,410

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

6a64fcfb57fbe6dc77aa75e60966d970885f42c36debaa7f7bf955dbc8920389

Transactions (2)

Coinbasec1e1ae04c963cb…86760b32f79b5b

1 in → 1 out9.1600 XPM116 B

AbwWkWZt…kawDhufa

73d03b88c3f35e…1657f2fd89d63f

1 in → 1 out2.9978 XPM192 B

Af1415qo…scuPteQ8

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.

6.008 × 10⁹¹(92-digit number)

60082348665594178521…67243676778024566159

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

6.008 × 10⁹¹(92-digit number)

60082348665594178521…67243676778024566159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.008 × 10⁹¹(92-digit number)

60082348665594178521…67243676778024566161

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

1.201 × 10⁹²(93-digit number)

12016469733118835704…34487353556049132319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.201 × 10⁹²(93-digit number)

12016469733118835704…34487353556049132321

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

2.403 × 10⁹²(93-digit number)

24032939466237671408…68974707112098264639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.403 × 10⁹²(93-digit number)

24032939466237671408…68974707112098264641

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

4.806 × 10⁹²(93-digit number)

48065878932475342817…37949414224196529279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.806 × 10⁹²(93-digit number)

48065878932475342817…37949414224196529281

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

9.613 × 10⁹²(93-digit number)

96131757864950685634…75898828448393058559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.613 × 10⁹²(93-digit number)

96131757864950685634…75898828448393058561

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 #370,204

Cookie Preferences