Block #381,401

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/29/2014, 11:25:07 PM · Difficulty 10.4063 · 6,417,519 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d11b0728d394fb1f28b0e3ddb6d47a4bc53f1d23cb7f10827eee79a6586c8368

View on Chainz ↗

Height

#381,401

Difficulty

10.406341

Transactions

Size

3.22 KB

Version

Bits

0a6805f2

Nonce

36,884

Timestamp

1/29/2014, 11:25:07 PM

Confirmations

6,417,519

Mined by

⛏️ aR-AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

5e845323f17eb952c8184fba2d6058d64e4f1f136690e211b5fb4cd9449a9584

Transactions (4)

Coinbasea88520c1821cc5…020409dcc8c8b3

1 in → 25 out9.2200 XPM913 B

AQvZBsUo…hppgRZTJ AFutDVqJ…TJTJj6UF AGKhfQo2…h7fBXLX6 ATKK7iFz…wZm46KN1 AGQxR1oS…2N1xAZXN

77e9b053d40d9b…a3ab61c8fdaab7

3 in → 10 out27.6200 XPM689 B

AY9ZSzfP…Yjc4XBCp AZcemWdf…BCToebsB AKenziQA…jfhjbJcR AZo9yWxU…q8ERX66m ASvbnyvb…4CP8B7rG

3eff58f8908e4d…db4a3ab1886108

4 in → 1 out4.0013 XPM638 B

AaYPiekK…vLRRTLhn

0fbfc63af49a7a…7ccc5fd9bf71a5

6 in → 2 out22.0907 XPM965 B

AMgamQfC…KWL2tuX9 AUPRT9rw…WqvyuSKL

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.

2.824 × 10⁹⁶(97-digit number)

28249653992056367597…44157227953791672319

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

2.824 × 10⁹⁶(97-digit number)

28249653992056367597…44157227953791672319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.824 × 10⁹⁶(97-digit number)

28249653992056367597…44157227953791672321

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

5.649 × 10⁹⁶(97-digit number)

56499307984112735194…88314455907583344639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.649 × 10⁹⁶(97-digit number)

56499307984112735194…88314455907583344641

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

1.129 × 10⁹⁷(98-digit number)

11299861596822547038…76628911815166689279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.129 × 10⁹⁷(98-digit number)

11299861596822547038…76628911815166689281

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

2.259 × 10⁹⁷(98-digit number)

22599723193645094077…53257823630333378559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.259 × 10⁹⁷(98-digit number)

22599723193645094077…53257823630333378561

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

4.519 × 10⁹⁷(98-digit number)

45199446387290188155…06515647260666757119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.519 × 10⁹⁷(98-digit number)

45199446387290188155…06515647260666757121

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