Block #494,136

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/16/2014, 12:55:34 AM · Difficulty 10.7130 · 6,313,893 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6319066d2c86e84073683d8c75cc3bbd7b07401f032d831b251805603726b0e4

View on Chainz ↗

Height

#494,136

Difficulty

10.712977

Transactions

Size

831 B

Version

Bits

0ab685a5

Nonce

30,832

Timestamp

4/16/2014, 12:55:34 AM

Confirmations

6,313,893

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

4edcda67c95210d852e8fdc6754efed74627383d020c6375ec9b970f78322353

Transactions (2)

Coinbasec4750a96473b75…7c19f21590f585

1 in → 1 out8.7100 XPM116 B

AbwWkWZt…kawDhufa

09bd9d1a5373ed…aafb5b195358e1

3 in → 7 out18.9775 XPM624 B

AQ8rAY3V…anzVDEuW AeKNrjNj…1NEq95Ta AMeyeZ9L…gJoDemgf AL9UZuKj…g3Q3eciV AQDGVS66…1PTWdWkm

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.

4.800 × 10⁹⁷(98-digit number)

48007980358298739736…70931380176466339999

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

4.800 × 10⁹⁷(98-digit number)

48007980358298739736…70931380176466339999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.800 × 10⁹⁷(98-digit number)

48007980358298739736…70931380176466340001

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

9.601 × 10⁹⁷(98-digit number)

96015960716597479473…41862760352932679999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.601 × 10⁹⁷(98-digit number)

96015960716597479473…41862760352932680001

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

1.920 × 10⁹⁸(99-digit number)

19203192143319495894…83725520705865359999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.920 × 10⁹⁸(99-digit number)

19203192143319495894…83725520705865360001

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

3.840 × 10⁹⁸(99-digit number)

38406384286638991789…67451041411730719999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.840 × 10⁹⁸(99-digit number)

38406384286638991789…67451041411730720001

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

7.681 × 10⁹⁸(99-digit number)

76812768573277983579…34902082823461439999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.681 × 10⁹⁸(99-digit number)

76812768573277983579…34902082823461440001

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 #494,136

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