Block #479,359

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/7/2014, 3:34:43 PM · Difficulty 10.5053 · 6,328,760 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

14a6211811b1be9095718e9e7276412b06c0d2395a5c5586f38a600f91d7fb64

View on Chainz ↗

Height

#479,359

Difficulty

10.505303

Transactions

Size

8.05 KB

Version

Bits

0a815b87

Nonce

3,495,506,740

Timestamp

4/7/2014, 3:34:43 PM

Confirmations

6,328,760

Mined by

⛏️ P2SHAaF35BdgXMHVDU9mVYY3FYsx7CxFY2Heoo

Merkle Root

c7c319a54fd7d475efa8238ddd200896c3e67c102b092be5f4e66147c812748e

Transactions (4)

Coinbasebdb0ae507d8f86…888f2e35e0a597

1 in → 1 out9.1500 XPM109 B

AaF35Bdg…xFY2Heoo

6301461cecf8a4…4d878423e7b400

16 in → 62 out142.7556 XPM4.38 KB

APQCLq5D…cpNbYpoy AUkdqaxr…4jcbMUQ7 AKfwEQcv…uF2f3oRH AcKeq82d…Ym6LNchU AHRnoPQw…SLFKBYxM

79270e7699578e…a564f5e4359ed8

22 in → 2 out75.6589 XPM3.26 KB

AX7GSbDT…95YeGybL AeViZaDT…hdPZPm53

1036554428b401…93ba58c33882c6

1 in → 2 out5.0217 XPM226 B

AThMwxNw…1NwfXbkL AZAVuoDZ…bNFYpgfR

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.

1.295 × 10⁹⁶(97-digit number)

12959883744087544264…54437682043507137279

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

1.295 × 10⁹⁶(97-digit number)

12959883744087544264…54437682043507137279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.295 × 10⁹⁶(97-digit number)

12959883744087544264…54437682043507137281

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

2.591 × 10⁹⁶(97-digit number)

25919767488175088528…08875364087014274559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.591 × 10⁹⁶(97-digit number)

25919767488175088528…08875364087014274561

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

5.183 × 10⁹⁶(97-digit number)

51839534976350177057…17750728174028549119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.183 × 10⁹⁶(97-digit number)

51839534976350177057…17750728174028549121

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

1.036 × 10⁹⁷(98-digit number)

10367906995270035411…35501456348057098239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.036 × 10⁹⁷(98-digit number)

10367906995270035411…35501456348057098241

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

2.073 × 10⁹⁷(98-digit number)

20735813990540070823…71002912696114196479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.073 × 10⁹⁷(98-digit number)

20735813990540070823…71002912696114196481

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 #479,359

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