Block #376,825

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/26/2014, 4:21:09 PM · Difficulty 10.4251 · 6,421,960 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

09ef8c1f21410af0d2530a51600e71c88925e059f0c0d7464c9b0bac89c1d751

View on Chainz ↗

Height

#376,825

Difficulty

10.425060

Transactions

Size

4.08 KB

Version

Bits

0a6cd0c1

Nonce

32,422

Timestamp

1/26/2014, 4:21:09 PM

Confirmations

6,421,960

Mined by

⛏️ aR5BAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

ecbf7a477f4970b5bb7902c0bbe0adfa34c41bc46d078d62fa08bb3d089063f6

Transactions (4)

Coinbased201d26fe04e30…d1de5b0b83a314

1 in → 21 out9.1900 XPM777 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH

fd729e2fdfbf43…635975d4c606af

3 in → 2 out102.8084 XPM520 B

AQYbSNRU…WxLCPW5A AVPAKZ11…o8EkXE1E

e52b25b29b6fbf…ee199faa7b6916

1 in → 2 out12.8486 XPM227 B

Ad4yrvtv…reCk5nnD AaguoHVJ…LbMfywdZ

fd0c070866c064…ba1a42b2c4a7ca

17 in → 1 out48.9195 XPM2.50 KB

AJx9ZjqR…dw5posZ5

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.

8.490 × 10⁹³(94-digit number)

84901750009288984146…78207860578402995199

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

8.490 × 10⁹³(94-digit number)

84901750009288984146…78207860578402995199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.490 × 10⁹³(94-digit number)

84901750009288984146…78207860578402995201

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

1.698 × 10⁹⁴(95-digit number)

16980350001857796829…56415721156805990399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.698 × 10⁹⁴(95-digit number)

16980350001857796829…56415721156805990401

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

3.396 × 10⁹⁴(95-digit number)

33960700003715593658…12831442313611980799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.396 × 10⁹⁴(95-digit number)

33960700003715593658…12831442313611980801

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

6.792 × 10⁹⁴(95-digit number)

67921400007431187317…25662884627223961599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.792 × 10⁹⁴(95-digit number)

67921400007431187317…25662884627223961601

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

1.358 × 10⁹⁵(96-digit number)

13584280001486237463…51325769254447923199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.358 × 10⁹⁵(96-digit number)

13584280001486237463…51325769254447923201

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