Block #372,755

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/23/2014, 8:15:27 PM · Difficulty 10.4260 · 6,438,144 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

39d93c51b79adb3659f3b31195bae6059c293a7e09aeaac0f4b7e5ccbf2d67e6

View on Chainz ↗

Height

#372,755

Difficulty

10.425990

Transactions

Size

436 B

Version

Bits

0a6d0dae

Nonce

19,842

Timestamp

1/23/2014, 8:15:27 PM

Confirmations

6,438,144

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

c82a2f719c86b49736232a1b0605d7010af5a537a9606a1e311a61d8f4b2b855

Transactions (2)

Coinbase3786fa7e892525…fddab20a06984a

1 in → 1 out9.2000 XPM116 B

AbwWkWZt…kawDhufa

891f0c08d8d6f8…28e1bf7928a9b1

1 in → 2 out2.9906 XPM226 B

AbSdrdeb…MA83pf8y AWqeLAbV…fpe1Fr2i

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.

2.434 × 10¹⁰³(104-digit number)

24345801443139595311…29607981958810931199

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

2.434 × 10¹⁰³(104-digit number)

24345801443139595311…29607981958810931199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.434 × 10¹⁰³(104-digit number)

24345801443139595311…29607981958810931201

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

4.869 × 10¹⁰³(104-digit number)

48691602886279190622…59215963917621862399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.869 × 10¹⁰³(104-digit number)

48691602886279190622…59215963917621862401

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

9.738 × 10¹⁰³(104-digit number)

97383205772558381245…18431927835243724799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.738 × 10¹⁰³(104-digit number)

97383205772558381245…18431927835243724801

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

1.947 × 10¹⁰⁴(105-digit number)

19476641154511676249…36863855670487449599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.947 × 10¹⁰⁴(105-digit number)

19476641154511676249…36863855670487449601

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

3.895 × 10¹⁰⁴(105-digit number)

38953282309023352498…73727711340974899199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.895 × 10¹⁰⁴(105-digit number)

38953282309023352498…73727711340974899201

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 #372,755

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