Block #2,647,791

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/4/2018, 3:11:07 AM · Difficulty 11.7625 · 4,186,113 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b0b3b7bbe65964597080e28052cf86966eca7078f9b281d3b70e99b055e65a12

View on Chainz ↗

Height

#2,647,791

Difficulty

11.762451

Transactions

Size

871 B

Version

Bits

0bc33005

Nonce

789,099,707

Timestamp

5/4/2018, 3:11:07 AM

Confirmations

4,186,113

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

378dac3e68255926eed2949f5c7d967c6af95e86ffad81e27ac5d7a276330dad

Transactions (2)

Coinbasee8ef00461c6afb…0531c9d0ad5f9d

1 in → 1 out7.2300 XPM110 B

Adqah8zh…1WwoHJ9t

cafebfa6a1259b…398d73b89ce4c0

4 in → 2 out550.0200 XPM670 B

AbvcsoUi…dNjo9yX2 AekUjb7w…cdXyeHDq

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.

2.052 × 10⁹⁶(97-digit number)

20523693695230652753…68504036148461132799

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

2.052 × 10⁹⁶(97-digit number)

20523693695230652753…68504036148461132799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.052 × 10⁹⁶(97-digit number)

20523693695230652753…68504036148461132801

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

4.104 × 10⁹⁶(97-digit number)

41047387390461305507…37008072296922265599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.104 × 10⁹⁶(97-digit number)

41047387390461305507…37008072296922265601

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

8.209 × 10⁹⁶(97-digit number)

82094774780922611015…74016144593844531199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.209 × 10⁹⁶(97-digit number)

82094774780922611015…74016144593844531201

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

1.641 × 10⁹⁷(98-digit number)

16418954956184522203…48032289187689062399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.641 × 10⁹⁷(98-digit number)

16418954956184522203…48032289187689062401

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

3.283 × 10⁹⁷(98-digit number)

32837909912369044406…96064578375378124799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.283 × 10⁹⁷(98-digit number)

32837909912369044406…96064578375378124801

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

6.567 × 10⁹⁷(98-digit number)

65675819824738088812…92129156750756249599

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 #2,647,791

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