Block #493,768

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/15/2014, 8:27:07 PM · Difficulty 10.7071 · 6,332,534 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3cac5ad0441f9d0edc4b810dbdad028b42b653a64ad96f9060345e078029b33c

View on Chainz ↗

Height

#493,768

Difficulty

10.707141

Transactions

Size

208 B

Version

Bits

0ab50735

Nonce

282,060,641

Timestamp

4/15/2014, 8:27:07 PM

Confirmations

6,332,534

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

5967b7171b57458b483d5ff3ed62ecacace6f89a108768dd9fbee2ab73c25693

Transactions (1)

Coinbase5967b7171b5745…bee2ab73c25693

1 in → 1 out8.7100 XPM116 B

AbwWkWZt…kawDhufa

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.

8.389 × 10⁹⁹(100-digit number)

83895189259247090204…41802693479942297599

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

8.389 × 10⁹⁹(100-digit number)

83895189259247090204…41802693479942297599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.389 × 10⁹⁹(100-digit number)

83895189259247090204…41802693479942297601

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

1.677 × 10¹⁰⁰(101-digit number)

16779037851849418040…83605386959884595199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.677 × 10¹⁰⁰(101-digit number)

16779037851849418040…83605386959884595201

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

3.355 × 10¹⁰⁰(101-digit number)

33558075703698836081…67210773919769190399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.355 × 10¹⁰⁰(101-digit number)

33558075703698836081…67210773919769190401

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

6.711 × 10¹⁰⁰(101-digit number)

67116151407397672163…34421547839538380799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.711 × 10¹⁰⁰(101-digit number)

67116151407397672163…34421547839538380801

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

1.342 × 10¹⁰¹(102-digit number)

13423230281479534432…68843095679076761599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.342 × 10¹⁰¹(102-digit number)

13423230281479534432…68843095679076761601

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 #493,768

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