Block #2,637,722

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/30/2018, 12:51:17 AM · Difficulty 11.4563 · 4,195,817 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0ce1b25e3615b3b7f23b8619cc9cefa1794e0e2fea31e2a4e92333c169329aee

View on Chainz ↗

Height

#2,637,722

Difficulty

11.456301

Transactions

Size

426 B

Version

Bits

0b74d01d

Nonce

4,373,439

Timestamp

4/30/2018, 12:51:17 AM

Confirmations

4,195,817

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

9a44d290f23733b98fbd9d16c7ff2a556cca40e4abc610e58f6e8470ffb6ad22

Transactions (2)

Coinbase8de47ca0684b46…fb01b6e66e4030

1 in → 1 out7.6200 XPM110 B

Adqah8zh…1WwoHJ9t

545e314e81325e…9761d2f4fa071a

1 in → 2 out5752.8736 XPM225 B

AVaQtWgv…EdQEqULx ALX1kUCY…kgDkbbFY

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.

3.479 × 10⁹⁷(98-digit number)

34795787334391065980…54743476718527303679

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

3.479 × 10⁹⁷(98-digit number)

34795787334391065980…54743476718527303679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.479 × 10⁹⁷(98-digit number)

34795787334391065980…54743476718527303681

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

6.959 × 10⁹⁷(98-digit number)

69591574668782131960…09486953437054607359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.959 × 10⁹⁷(98-digit number)

69591574668782131960…09486953437054607361

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

1.391 × 10⁹⁸(99-digit number)

13918314933756426392…18973906874109214719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.391 × 10⁹⁸(99-digit number)

13918314933756426392…18973906874109214721

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

2.783 × 10⁹⁸(99-digit number)

27836629867512852784…37947813748218429439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.783 × 10⁹⁸(99-digit number)

27836629867512852784…37947813748218429441

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

5.567 × 10⁹⁸(99-digit number)

55673259735025705568…75895627496436858879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.567 × 10⁹⁸(99-digit number)

55673259735025705568…75895627496436858881

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

1.113 × 10⁹⁹(100-digit number)

11134651947005141113…51791254992873717759

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 #2,637,722

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