Block #844,670

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/8/2014, 7:12:49 AM · Difficulty 10.9729 · 5,988,439 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c3a3999bd3e4e228bc4ed25c54aa8716ac21419f406a4e1e2de4feccb7a0503e

View on Chainz ↗

Height

#844,670

Difficulty

10.972890

Transactions

Size

1.30 KB

Version

Bits

0af90f4c

Nonce

654,342,029

Timestamp

12/8/2014, 7:12:49 AM

Confirmations

5,988,439

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1398524b22ee443b14314bce5c31f72d9bfcb61faa68fe4da03519bb6d74e700

Transactions (4)

Coinbase5f7c6f8468abd7…83b812d707d91f

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

daef0d60a78ad1…84bc7d67884e9a

4 in → 2 out10.0725 XPM667 B

ATNAKXn4…gNAq5i7m AaCAKKXy…wyxKEaYm

7f1a8a618a0d1b…83d2d169c9d2dd

1 in → 2 out0.1222 XPM227 B

AMzkt3nU…AuyttKKE AJX7zqNw…H1adZSGa

91395ef6e35015…6ccd8d3a401381

1 in → 2 out0.0222 XPM226 B

ASZrKozC…zUXYMPMT AVt1RnUK…SRXfEbBH

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.

4.108 × 10⁹⁸(99-digit number)

41089380597808434378…58641757710697676799

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

4.108 × 10⁹⁸(99-digit number)

41089380597808434378…58641757710697676799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.108 × 10⁹⁸(99-digit number)

41089380597808434378…58641757710697676801

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

8.217 × 10⁹⁸(99-digit number)

82178761195616868757…17283515421395353599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.217 × 10⁹⁸(99-digit number)

82178761195616868757…17283515421395353601

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

1.643 × 10⁹⁹(100-digit number)

16435752239123373751…34567030842790707199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.643 × 10⁹⁹(100-digit number)

16435752239123373751…34567030842790707201

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

3.287 × 10⁹⁹(100-digit number)

32871504478246747503…69134061685581414399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.287 × 10⁹⁹(100-digit number)

32871504478246747503…69134061685581414401

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

6.574 × 10⁹⁹(100-digit number)

65743008956493495006…38268123371162828799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.574 × 10⁹⁹(100-digit number)

65743008956493495006…38268123371162828801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.314 × 10¹⁰⁰(101-digit number)

13148601791298699001…76536246742325657599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #844,670

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