Block #496,028

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/16/2014, 9:34:46 PM · Difficulty 10.7482 · 6,299,544 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b79f109ef2c433dd99c78f40b1654654c9f66f485fdac3cc2e52ea0a5478cf88

View on Chainz ↗

Height

#496,028

Difficulty

10.748190

Transactions

Size

2.84 KB

Version

Bits

0abf8965

Nonce

41,903,855

Timestamp

4/16/2014, 9:34:46 PM

Confirmations

6,299,544

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

48ad1552d910ec607d406e52c08d37bfa2395ef6a6fc03e2e2d183edf86f180a

Transactions (2)

Coinbase084a93fb3e50bc…f5ba019e7fe9ff

1 in → 1 out8.6700 XPM116 B

AbwWkWZt…kawDhufa

50a2a2af8d0e15…ff229e6509e33b

9 in → 40 out78.7707 XPM2.63 KB

AUkdqaxr…4jcbMUQ7 AKfwEQcv…uF2f3oRH ASqqpxAv…dTvgfRnF AQVXX7yy…4wJ5NQj4 AKzv8KjF…W6FeM9j1

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.

1.703 × 10⁹⁹(100-digit number)

17036825041278839741…99353251981339463679

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

1.703 × 10⁹⁹(100-digit number)

17036825041278839741…99353251981339463679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.703 × 10⁹⁹(100-digit number)

17036825041278839741…99353251981339463681

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

3.407 × 10⁹⁹(100-digit number)

34073650082557679483…98706503962678927359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.407 × 10⁹⁹(100-digit number)

34073650082557679483…98706503962678927361

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

6.814 × 10⁹⁹(100-digit number)

68147300165115358967…97413007925357854719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.814 × 10⁹⁹(100-digit number)

68147300165115358967…97413007925357854721

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

1.362 × 10¹⁰⁰(101-digit number)

13629460033023071793…94826015850715709439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.362 × 10¹⁰⁰(101-digit number)

13629460033023071793…94826015850715709441

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

2.725 × 10¹⁰⁰(101-digit number)

27258920066046143587…89652031701431418879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.725 × 10¹⁰⁰(101-digit number)

27258920066046143587…89652031701431418881

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