Block #381,356

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/29/2014, 10:52:18 PM · Difficulty 10.4060 · 6,410,199 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b2fe83ba704a78f026ff50d6f3174e6270da0a10b9e73d060cd46567926a4453

View on Chainz ↗

Height

#381,356

Difficulty

10.405962

Transactions

Size

900 B

Version

Bits

0a67ed28

Nonce

9,716

Timestamp

1/29/2014, 10:52:18 PM

Confirmations

6,410,199

Merkle Root

e306cf148bc2e24932c03c25ba58cfeeda787b94cf6c2dff45e6e2421c3b253d

Transactions (4)

Coinbase59180013bf8326…81bcaf55a5e655

1 in → 2 out9.2500 XPM131 B

Ac2JYASP…tcBL5PEW AJno7LX2…vo4wdWtY

d88f7975ffafa9…24233d16432179

1 in → 2 out8.1237 XPM226 B

ARijjV4A…TpVV5Jq7 AcZiSGp1…qwj4QX3k

5c494c0eb3803e…703f7c816587bc

1 in → 2 out6.1281 XPM226 B

AMU8nEj9…Eo32pqxr AQaQCYrJ…Bg6kM1HC

2d9dfd650dc50d…f68fe4812f4117

1 in → 2 out4.1352 XPM227 B

AJjsX4t4…gtmJp9SX AKL5J3vt…zS66bjYZ

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.

1.028 × 10⁹⁵(96-digit number)

10281123769303089116…58392325035640486399

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

1.028 × 10⁹⁵(96-digit number)

10281123769303089116…58392325035640486399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.028 × 10⁹⁵(96-digit number)

10281123769303089116…58392325035640486401

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

2.056 × 10⁹⁵(96-digit number)

20562247538606178233…16784650071280972799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.056 × 10⁹⁵(96-digit number)

20562247538606178233…16784650071280972801

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

4.112 × 10⁹⁵(96-digit number)

41124495077212356467…33569300142561945599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.112 × 10⁹⁵(96-digit number)

41124495077212356467…33569300142561945601

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

8.224 × 10⁹⁵(96-digit number)

82248990154424712935…67138600285123891199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.224 × 10⁹⁵(96-digit number)

82248990154424712935…67138600285123891201

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

1.644 × 10⁹⁶(97-digit number)

16449798030884942587…34277200570247782399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.644 × 10⁹⁶(97-digit number)

16449798030884942587…34277200570247782401

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