Block #2,643,241

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/2/2018, 12:57:39 AM · Difficulty 11.6776 · 4,163,575 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5ad2dc6c903f247034e6a6649ec741515930dea0be9b74959eae2363c1ed3748

View on Chainz ↗

Height

#2,643,241

Difficulty

11.677644

Transactions

Size

2.21 KB

Version

Bits

0bad7a0c

Nonce

256,448,551

Timestamp

5/2/2018, 12:57:39 AM

Confirmations

4,163,575

Mined by

⛏️ P2SHAPzT7zqJqLgVWZDWcKHnZQqfyiwYP3bXjo

Merkle Root

79b8f0481a253f47f5fc299a04c4999c92544c159e46a79886de6fdad6cf17a0

Transactions (5)

Coinbase1f82f6f5007ba6…99fa5a045f9059

1 in → 1 out7.3700 XPM110 B

APzT7zqJ…wYP3bXjo

b46d10526c24f5…509e3910d40b18

1 in → 1 out299.9900 XPM192 B

ANyzqvMw…7TTfPBz6

aa78e0f091ec62…b10a9a9382d6fb

8 in → 2 out31.9800 XPM1.23 KB

AZqnyE61…HsB7HLeU AWqa1nJF…bmHSzvat

586dc9d92d9a8b…bb32efc69a6103

1 in → 2 out4.6766 XPM227 B

AZxdjt1n…kN28cixg AJ64A3i2…UjNpZxDY

a954c1d9a89d87…2f1f5d32615edd

2 in → 2 out1.2814 XPM374 B

AetdEEeF…H6T3c6Hf AMGPqZrT…2dirCkMK

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.

9.987 × 10⁹⁸(99-digit number)

99877283653636674506…00404870790342574079

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

9.987 × 10⁹⁸(99-digit number)

99877283653636674506…00404870790342574079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.987 × 10⁹⁸(99-digit number)

99877283653636674506…00404870790342574081

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

1.997 × 10⁹⁹(100-digit number)

19975456730727334901…00809741580685148159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.997 × 10⁹⁹(100-digit number)

19975456730727334901…00809741580685148161

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

3.995 × 10⁹⁹(100-digit number)

39950913461454669802…01619483161370296319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.995 × 10⁹⁹(100-digit number)

39950913461454669802…01619483161370296321

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

7.990 × 10⁹⁹(100-digit number)

79901826922909339605…03238966322740592639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.990 × 10⁹⁹(100-digit number)

79901826922909339605…03238966322740592641

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

1.598 × 10¹⁰⁰(101-digit number)

15980365384581867921…06477932645481185279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.598 × 10¹⁰⁰(101-digit number)

15980365384581867921…06477932645481185281

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

3.196 × 10¹⁰⁰(101-digit number)

31960730769163735842…12955865290962370559

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 #2,643,241

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