Block #2,642,496

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/1/2018, 6:26:05 PM · Difficulty 11.6542 · 4,189,206 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6cda43cc630372bd59fada057f86ff772cafa10ccf84f0a3ec5bfbfcb784ce5e

View on Chainz ↗

Height

#2,642,496

Difficulty

11.654186

Transactions

Size

425 B

Version

Bits

0ba778b5

Nonce

1,337,013,165

Timestamp

5/1/2018, 6:26:05 PM

Confirmations

4,189,206

Mined by

⛏️ P2SHAKDtw63a28BJ1fPKRAaCHTpapsA4iz8TJQ

Merkle Root

f8d4f15b562206a956ff3bdaa4188540b7ced924a2832e2a585a8d8847ce42b7

Transactions (2)

Coinbasefb12ee49fff3ad…0ba17290d85b6a

1 in → 1 out7.3600 XPM110 B

AKDtw63a…A4iz8TJQ

5b55be39fa878a…82c3e5ce81381e

1 in → 2 out36.8203 XPM225 B

AHZos9sZ…mwgjHLSH AGLGGXLb…kGmRHvYo

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.

1.245 × 10⁹⁴(95-digit number)

12458194930526585841…92397405208658396199

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

1.245 × 10⁹⁴(95-digit number)

12458194930526585841…92397405208658396199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.245 × 10⁹⁴(95-digit number)

12458194930526585841…92397405208658396201

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

2.491 × 10⁹⁴(95-digit number)

24916389861053171682…84794810417316792399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.491 × 10⁹⁴(95-digit number)

24916389861053171682…84794810417316792401

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

4.983 × 10⁹⁴(95-digit number)

49832779722106343364…69589620834633584799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.983 × 10⁹⁴(95-digit number)

49832779722106343364…69589620834633584801

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

9.966 × 10⁹⁴(95-digit number)

99665559444212686729…39179241669267169599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.966 × 10⁹⁴(95-digit number)

99665559444212686729…39179241669267169601

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

1.993 × 10⁹⁵(96-digit number)

19933111888842537345…78358483338534339199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.993 × 10⁹⁵(96-digit number)

19933111888842537345…78358483338534339201

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

3.986 × 10⁹⁵(96-digit number)

39866223777685074691…56716966677068678399

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 #2,642,496

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