Block #382,648

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/30/2014, 9:03:16 PM · Difficulty 10.4009 · 6,411,813 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6ce3175592a258dcaa761e7a8c72012a675f9aeb2f90f687af5a5ac4d9d507c9

View on Chainz ↗

Height

#382,648

Difficulty

10.400924

Transactions

Size

1.01 KB

Version

Bits

0a66a2fa

Nonce

207,843

Timestamp

1/30/2014, 9:03:16 PM

Confirmations

6,411,813

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

0d8cfad5528535903aae3a5fe7788b36c37da6aa20927dc2bd8d658bf2e99031

Transactions (4)

Coinbaseaca986b2f59707…483e70747f9851

1 in → 1 out9.2600 XPM116 B

AbwWkWZt…kawDhufa

b250be97397962…7fc3c6797c8e31

2 in → 2 out16.4179 XPM374 B

AHJZe99R…VN5agbar AZj7eRYU…vjX8YCX5

53ead53087b843…0c3b25f05dce28

1 in → 2 out2.9009 XPM227 B

ASjiXEcS…25aHfhAC AeebkcCv…64y2XWbS

eff58b727bed6c…d1dfb85db78a24

1 in → 2 out1.1000 XPM227 B

AdAabxCb…6N16D3m7 AH5uh1YE…SUhNy1ip

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.

4.132 × 10⁹⁵(96-digit number)

41328375556776039782…74991932135280153599

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

4.132 × 10⁹⁵(96-digit number)

41328375556776039782…74991932135280153599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.132 × 10⁹⁵(96-digit number)

41328375556776039782…74991932135280153601

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

8.265 × 10⁹⁵(96-digit number)

82656751113552079565…49983864270560307199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.265 × 10⁹⁵(96-digit number)

82656751113552079565…49983864270560307201

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

1.653 × 10⁹⁶(97-digit number)

16531350222710415913…99967728541120614399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.653 × 10⁹⁶(97-digit number)

16531350222710415913…99967728541120614401

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

3.306 × 10⁹⁶(97-digit number)

33062700445420831826…99935457082241228799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.306 × 10⁹⁶(97-digit number)

33062700445420831826…99935457082241228801

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

6.612 × 10⁹⁶(97-digit number)

66125400890841663652…99870914164482457599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.612 × 10⁹⁶(97-digit number)

66125400890841663652…99870914164482457601

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