Block #787,662

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/29/2014, 5:24:20 AM · Difficulty 10.9746 · 6,021,960 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cac1fbad7c8d56e3322d43d6d700dd862067c4de2d906e37fa75fa21d55229cf

View on Chainz ↗

Height

#787,662

Difficulty

10.974589

Transactions

Size

51.21 KB

Version

Bits

0af97eb0

Nonce

769,734,175

Timestamp

10/29/2014, 5:24:20 AM

Confirmations

6,021,960

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e4016499dff31ce7ffd1e52ab77f53a8f51e50ac06f5b9e93377e9a59e39c900

Transactions (3)

Coinbase95e42635a56fec…baaade838e6399

1 in → 1 out8.9900 XPM116 B

ANSXnLY2…Sd25TjkD

5a8c9b3226aed6…c937127908d38d

351 in → 2 out100000.0100 XPM50.78 KB

ATNFg4tq…AMdaKJFH AUN6jDF8…RmrvS66u

6bdf84f64a2625…1cc105853cdb7b

1 in → 2 out1.9005 XPM226 B

AZbSskNP…cvhyZN6F AMoJsji6…a13Bp22Q

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.

7.620 × 10⁹⁶(97-digit number)

76206622766943535547…39460876441018974079

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

7.620 × 10⁹⁶(97-digit number)

76206622766943535547…39460876441018974079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.620 × 10⁹⁶(97-digit number)

76206622766943535547…39460876441018974081

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

1.524 × 10⁹⁷(98-digit number)

15241324553388707109…78921752882037948159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.524 × 10⁹⁷(98-digit number)

15241324553388707109…78921752882037948161

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

3.048 × 10⁹⁷(98-digit number)

30482649106777414219…57843505764075896319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.048 × 10⁹⁷(98-digit number)

30482649106777414219…57843505764075896321

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

6.096 × 10⁹⁷(98-digit number)

60965298213554828438…15687011528151792639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.096 × 10⁹⁷(98-digit number)

60965298213554828438…15687011528151792641

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

1.219 × 10⁹⁸(99-digit number)

12193059642710965687…31374023056303585279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.219 × 10⁹⁸(99-digit number)

12193059642710965687…31374023056303585281

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 #787,662

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