Block #408,851

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/17/2014, 11:36:44 PM · Difficulty 10.4261 · 6,416,686 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3d1ffe96038381fa0c946c87ee30b9e6e8b83eccd0de55792f0eb58aa10d69f2

View on Chainz ↗

Height

#408,851

Difficulty

10.426149

Transactions

Size

399 B

Version

Bits

0a6d181d

Nonce

503,317,873

Timestamp

2/17/2014, 11:36:44 PM

Confirmations

6,416,686

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

eec1dfac04d0a0980956691205e01110c39d8935151db81f1cef8998cd96223d

Transactions (2)

Coinbase8809685f43172d…5f8b45ef0f8dfb

1 in → 1 out9.2000 XPM116 B

AbwWkWZt…kawDhufa

7797e49d15de09…29394e3e0c33d5

1 in → 1 out0.2200 XPM193 B

ASZJkfqV…jr3pSKXk

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.

4.196 × 10⁹⁵(96-digit number)

41969028137162154626…21085655462151788719

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

4.196 × 10⁹⁵(96-digit number)

41969028137162154626…21085655462151788719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.196 × 10⁹⁵(96-digit number)

41969028137162154626…21085655462151788721

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

8.393 × 10⁹⁵(96-digit number)

83938056274324309252…42171310924303577439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.393 × 10⁹⁵(96-digit number)

83938056274324309252…42171310924303577441

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

1.678 × 10⁹⁶(97-digit number)

16787611254864861850…84342621848607154879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.678 × 10⁹⁶(97-digit number)

16787611254864861850…84342621848607154881

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

3.357 × 10⁹⁶(97-digit number)

33575222509729723700…68685243697214309759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.357 × 10⁹⁶(97-digit number)

33575222509729723700…68685243697214309761

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

6.715 × 10⁹⁶(97-digit number)

67150445019459447401…37370487394428619519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.715 × 10⁹⁶(97-digit number)

67150445019459447401…37370487394428619521

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 #408,851

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