Block #494,009

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/15/2014, 11:12:35 PM · Difficulty 10.7116 · 6,320,885 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

106c6ddc17fb473f916dbe35bbe986b6d5fc63f2d61270f36575f5e905b77236

View on Chainz ↗

Height

#494,009

Difficulty

10.711622

Transactions

Size

868 B

Version

Bits

0ab62cda

Nonce

32,276

Timestamp

4/15/2014, 11:12:35 PM

Confirmations

6,320,885

Mined by

ASgUri65LPNF7m3R7v9tApccHyC7NLcyBg

Merkle Root

1e07c280e6bc6b2e6e55455d621a29edeb3fdd45c755c2a2d2abf9f0fc18677f

Transactions (1)

Coinbase1e07c280e6bc6b…abf9f0fc18677f

1 in → 21 out8.7000 XPM777 B

ASgUri65…C7NLcyBg AGz9gyZW…bo8NYQpw AdFLJFhb…bsaVkAyh ATp4jJhs…TbSgR8Qb Adbb4svj…dQWTHsq5

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.

1.974 × 10⁹⁸(99-digit number)

19743374337018258897…98290627637869203839

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

1.974 × 10⁹⁸(99-digit number)

19743374337018258897…98290627637869203839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.974 × 10⁹⁸(99-digit number)

19743374337018258897…98290627637869203841

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

3.948 × 10⁹⁸(99-digit number)

39486748674036517794…96581255275738407679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.948 × 10⁹⁸(99-digit number)

39486748674036517794…96581255275738407681

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

7.897 × 10⁹⁸(99-digit number)

78973497348073035588…93162510551476815359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.897 × 10⁹⁸(99-digit number)

78973497348073035588…93162510551476815361

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

1.579 × 10⁹⁹(100-digit number)

15794699469614607117…86325021102953630719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.579 × 10⁹⁹(100-digit number)

15794699469614607117…86325021102953630721

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

3.158 × 10⁹⁹(100-digit number)

31589398939229214235…72650042205907261439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.158 × 10⁹⁹(100-digit number)

31589398939229214235…72650042205907261441

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 #494,009

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