Block #779,547

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/23/2014, 1:31:44 AM · Difficulty 10.9779 · 6,037,625 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e01d544f869de17544a6f76cf9bce6aa5b3aa05a3de7e765008eaeeffdf1588d

View on Chainz ↗

Height

#779,547

Difficulty

10.977885

Transactions

Size

244 B

Version

Bits

0afa56b0

Nonce

550,488,706

Timestamp

10/23/2014, 1:31:44 AM

Confirmations

6,037,625

Mined by

⛏️ P2SHAYFivgcJEqUfH1zEbfNs35USz3FT8wELGF

Merkle Root

f93fb366b9978a62fc2bdb3f94b2a22e9ab16a69d00658bc4b293a331a55264e

Transactions (1)

Coinbasef93fb366b9978a…293a331a55264e

1 in → 2 out8.2800 XPM152 B

AYFivgcJ…FT8wELGF ALPu3s2c…EJXLjVFh

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.

8.674 × 10⁹⁸(99-digit number)

86741323610475239534…62945555315060735999

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

8.674 × 10⁹⁸(99-digit number)

86741323610475239534…62945555315060735999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.674 × 10⁹⁸(99-digit number)

86741323610475239534…62945555315060736001

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

1.734 × 10⁹⁹(100-digit number)

17348264722095047906…25891110630121471999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.734 × 10⁹⁹(100-digit number)

17348264722095047906…25891110630121472001

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

3.469 × 10⁹⁹(100-digit number)

34696529444190095813…51782221260242943999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.469 × 10⁹⁹(100-digit number)

34696529444190095813…51782221260242944001

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

6.939 × 10⁹⁹(100-digit number)

69393058888380191627…03564442520485887999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.939 × 10⁹⁹(100-digit number)

69393058888380191627…03564442520485888001

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

1.387 × 10¹⁰⁰(101-digit number)

13878611777676038325…07128885040971775999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.387 × 10¹⁰⁰(101-digit number)

13878611777676038325…07128885040971776001

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 #779,547

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