Block #442,267

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/13/2014, 5:43:08 PM · Difficulty 10.3482 · 6,374,328 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9d81b5e5b9fb07c8502de5d13b95848e15ae03a7c608a4ffac6c99e51d676861

View on Chainz ↗

Height

#442,267

Difficulty

10.348189

Transactions

Size

1003 B

Version

Bits

0a5922f0

Nonce

102,030

Timestamp

3/13/2014, 5:43:08 PM

Confirmations

6,374,328

Mined by

⛏️ aS!cAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

2b1f8519577cfcc8e38d3bc366f191269d3475e21310b042278c55511e43a274

Transactions (1)

Coinbase2b1f8519577cfc…8c55511e43a274

1 in → 25 out9.3200 XPM913 B

AQvZBsUo…hppgRZTJ ATKK7iFz…wZm46KN1 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

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.

7.315 × 10⁹³(94-digit number)

73157460339470160771…21743340654656227899

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

7.315 × 10⁹³(94-digit number)

73157460339470160771…21743340654656227899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.315 × 10⁹³(94-digit number)

73157460339470160771…21743340654656227901

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

1.463 × 10⁹⁴(95-digit number)

14631492067894032154…43486681309312455799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.463 × 10⁹⁴(95-digit number)

14631492067894032154…43486681309312455801

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

2.926 × 10⁹⁴(95-digit number)

29262984135788064308…86973362618624911599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.926 × 10⁹⁴(95-digit number)

29262984135788064308…86973362618624911601

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

5.852 × 10⁹⁴(95-digit number)

58525968271576128617…73946725237249823199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.852 × 10⁹⁴(95-digit number)

58525968271576128617…73946725237249823201

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

1.170 × 10⁹⁵(96-digit number)

11705193654315225723…47893450474499646399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.170 × 10⁹⁵(96-digit number)

11705193654315225723…47893450474499646401

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

2.341 × 10⁹⁵(96-digit number)

23410387308630451446…95786900948999292799

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 #442,267

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