Block #2,641,360

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/1/2018, 7:55:47 AM · Difficulty 11.6176 · 4,189,524 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

074009d1f02c4c60dfdf6ac887e1ab915936431fdd0e2160af2205fe13daa02a

View on Chainz ↗

Height

#2,641,360

Difficulty

11.617619

Transactions

Size

393 B

Version

Bits

0b9e1c41

Nonce

1,590,372,061

Timestamp

5/1/2018, 7:55:47 AM

Confirmations

4,189,524

Mined by

⛏️ P2SHAcy9s5ZRkDrGegFkhPpP6xueHDVqGzwmis

Merkle Root

f4d38a24099d8127987b1f17234ae572eed49a9aa4edb7d639d5e5d17d7bbbf5

Transactions (2)

Coinbase8cf8564dc3191c…a06c2ef3dae6e9

1 in → 1 out7.4100 XPM110 B

Acy9s5ZR…VqGzwmis

f8d2e337598334…550f25cba3374e

1 in → 2 out7.5700 XPM192 B

AGRwRCLk…i3H1nRMT ATt8vVZX…8WgwsJUS

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.

4.648 × 10⁹⁷(98-digit number)

46486923350249162591…74042077629032038399

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

4.648 × 10⁹⁷(98-digit number)

46486923350249162591…74042077629032038399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.648 × 10⁹⁷(98-digit number)

46486923350249162591…74042077629032038401

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

9.297 × 10⁹⁷(98-digit number)

92973846700498325182…48084155258064076799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.297 × 10⁹⁷(98-digit number)

92973846700498325182…48084155258064076801

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

1.859 × 10⁹⁸(99-digit number)

18594769340099665036…96168310516128153599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.859 × 10⁹⁸(99-digit number)

18594769340099665036…96168310516128153601

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

3.718 × 10⁹⁸(99-digit number)

37189538680199330072…92336621032256307199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.718 × 10⁹⁸(99-digit number)

37189538680199330072…92336621032256307201

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

7.437 × 10⁹⁸(99-digit number)

74379077360398660145…84673242064512614399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.437 × 10⁹⁸(99-digit number)

74379077360398660145…84673242064512614401

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

1.487 × 10⁹⁹(100-digit number)

14875815472079732029…69346484129025228799

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 #2,641,360

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