Block #375,000

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/25/2014, 10:36:22 AM · Difficulty 10.4203 · 6,442,606 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

224c23cb68a86fc6260f880a0680e47dbf19259a77cfaa519e7350b41dd9b98b

View on Chainz ↗

Height

#375,000

Difficulty

10.420254

Transactions

Size

656 B

Version

Bits

0a6b95c7

Nonce

268,438,042

Timestamp

1/25/2014, 10:36:22 AM

Confirmations

6,442,606

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

ef814566fde72f4ad5c337630c55ea015440147b3eb846f53081f2273707ab57

Transactions (3)

Coinbase90f747b4b3e269…cacb07f78b9585

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

bf33a56bd1f24f…b640d9937a78ea

1 in → 2 out1.1015 XPM225 B

AS7avFou…jAo5C2sC AQDV8G49…VGqpnXjQ

d366bf55cec26f…b279810fd2a562

1 in → 2 out1.0721 XPM226 B

ALUp1h5z…F4fLZVLk AMU8nEj9…Eo32pqxr

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.

9.411 × 10⁹¹(92-digit number)

94112325160869971420…77118351002566829799

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

9.411 × 10⁹¹(92-digit number)

94112325160869971420…77118351002566829799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.411 × 10⁹¹(92-digit number)

94112325160869971420…77118351002566829801

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

1.882 × 10⁹²(93-digit number)

18822465032173994284…54236702005133659599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.882 × 10⁹²(93-digit number)

18822465032173994284…54236702005133659601

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

3.764 × 10⁹²(93-digit number)

37644930064347988568…08473404010267319199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.764 × 10⁹²(93-digit number)

37644930064347988568…08473404010267319201

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

7.528 × 10⁹²(93-digit number)

75289860128695977136…16946808020534638399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.528 × 10⁹²(93-digit number)

75289860128695977136…16946808020534638401

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

1.505 × 10⁹³(94-digit number)

15057972025739195427…33893616041069276799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.505 × 10⁹³(94-digit number)

15057972025739195427…33893616041069276801

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 #375,000

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