Block #467,422

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/30/2014, 6:52:11 PM · Difficulty 10.4351 · 6,343,348 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

95692524985daea3e734b65aa8058345ae308e1034d09b0ddf714dd02db27351

View on Chainz ↗

Height

#467,422

Difficulty

10.435133

Transactions

Size

1.08 KB

Version

Bits

0a6f64d8

Nonce

121,837

Timestamp

3/30/2014, 6:52:11 PM

Confirmations

6,343,348

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

8025aaf52609fb69d0567fe23565538cba6a0ed219cec5275ad657aa9fee51fe

Transactions (5)

Coinbase90cf722bf27e5c…6158b0a96c244a

1 in → 1 out9.2100 XPM116 B

AbwWkWZt…kawDhufa

1fc4ae248e8ac3…5b8835b252f79f

1 in → 2 out9.1900 XPM226 B

ATvgq3Rz…fHTvramX AVSJ9AM4…ahi6r144

58200e2eed0cdb…5dec2c8cee19f6

1 in → 2 out7.6629 XPM227 B

AWKFbfJm…XRb4582z AeB5HmMq…mCGHeD8p

6162e49c6279b0…404ed635ae4e07

1 in → 2 out7.1459 XPM226 B

ARnMhLt3…M5NY4WfV AMhVrz1v…yocj6Cob

42d435339fc641…08b6393d7e4853

1 in → 2 out2.1179 XPM226 B

AJ2ZsCr2…U5acAbaT AXZf8xqq…hQwCQgXt

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.

1.066 × 10⁹¹(92-digit number)

10660028280563546607…41902608870742455999

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

1.066 × 10⁹¹(92-digit number)

10660028280563546607…41902608870742455999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.066 × 10⁹¹(92-digit number)

10660028280563546607…41902608870742456001

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

2.132 × 10⁹¹(92-digit number)

21320056561127093214…83805217741484911999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.132 × 10⁹¹(92-digit number)

21320056561127093214…83805217741484912001

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

4.264 × 10⁹¹(92-digit number)

42640113122254186429…67610435482969823999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.264 × 10⁹¹(92-digit number)

42640113122254186429…67610435482969824001

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

8.528 × 10⁹¹(92-digit number)

85280226244508372858…35220870965939647999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.528 × 10⁹¹(92-digit number)

85280226244508372858…35220870965939648001

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

1.705 × 10⁹²(93-digit number)

17056045248901674571…70441741931879295999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.705 × 10⁹²(93-digit number)

17056045248901674571…70441741931879296001

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 #467,422

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