Block #2,780,543

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/5/2018, 5:33:35 PM · Difficulty 11.6496 · 4,056,088 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c84f684c2afa67a57173c94edcf54c431238b5e2c14917e965a46d40a1c4f2ba

View on Chainz ↗

Height

#2,780,543

Difficulty

11.649552

Transactions

Size

575 B

Version

Bits

0ba6490a

Nonce

494,633,600

Timestamp

8/5/2018, 5:33:35 PM

Confirmations

4,056,088

Mined by

⛏️ P2SHAYDGiWwmDXAGFWbP8V69QS8Pka59mPFzpv

Merkle Root

f5eeca19f4fddfbb2982ca522975288f1ca260dae8e88b907c560745c87efd02

Transactions (2)

Coinbase14626c9e758a37…d5b9b05bff7f0c

1 in → 1 out7.3700 XPM109 B

AYDGiWwm…59mPFzpv

ef116bd4ff9347…51654d742a59cb

2 in → 2 out174.6238 XPM376 B

AMacMFhM…iFNVuut4 Ab9Yjoqr…iQn6huSU

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.

5.849 × 10⁹⁵(96-digit number)

58491508140966101090…81929051294016848639

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

5.849 × 10⁹⁵(96-digit number)

58491508140966101090…81929051294016848639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.849 × 10⁹⁵(96-digit number)

58491508140966101090…81929051294016848641

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

1.169 × 10⁹⁶(97-digit number)

11698301628193220218…63858102588033697279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.169 × 10⁹⁶(97-digit number)

11698301628193220218…63858102588033697281

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

2.339 × 10⁹⁶(97-digit number)

23396603256386440436…27716205176067394559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.339 × 10⁹⁶(97-digit number)

23396603256386440436…27716205176067394561

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

4.679 × 10⁹⁶(97-digit number)

46793206512772880872…55432410352134789119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.679 × 10⁹⁶(97-digit number)

46793206512772880872…55432410352134789121

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

9.358 × 10⁹⁶(97-digit number)

93586413025545761744…10864820704269578239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.358 × 10⁹⁶(97-digit number)

93586413025545761744…10864820704269578241

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

1.871 × 10⁹⁷(98-digit number)

18717282605109152348…21729641408539156479

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 #2,780,543

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