Block #89,027

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/30/2013, 1:45:57 AM · Difficulty 9.2619 · 6,714,285 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e6be2e563b59d0d8ec88b34ba2d379b6d2992699c9b44bbd838d7ce363fb62eb

View on Chainz ↗

Height

#89,027

Difficulty

9.261938

Transactions

Size

208 B

Version

Bits

09430e64

Nonce

108,326

Timestamp

7/30/2013, 1:45:57 AM

Confirmations

6,714,285

Mined by

⛏️ P2SHAdGywN2wBfzQwTo7jGpVnaaNzDznNpTfrS

Merkle Root

0694262f9c0e2be8932b2c72aad5415de597a3e2b928c17d5f0aa31373890062

Transactions (1)

Coinbase0694262f9c0e2b…0aa31373890062

1 in → 1 out11.6400 XPM109 B

AdGywN2w…znNpTfrS

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.

9.375 × 10¹¹⁶(117-digit number)

93757874754643601732…05309158724916179239

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

9.375 × 10¹¹⁶(117-digit number)

93757874754643601732…05309158724916179239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.375 × 10¹¹⁶(117-digit number)

93757874754643601732…05309158724916179241

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

1.875 × 10¹¹⁷(118-digit number)

18751574950928720346…10618317449832358479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.875 × 10¹¹⁷(118-digit number)

18751574950928720346…10618317449832358481

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

3.750 × 10¹¹⁷(118-digit number)

37503149901857440692…21236634899664716959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.750 × 10¹¹⁷(118-digit number)

37503149901857440692…21236634899664716961

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

7.500 × 10¹¹⁷(118-digit number)

75006299803714881385…42473269799329433919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.500 × 10¹¹⁷(118-digit number)

75006299803714881385…42473269799329433921

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

1.500 × 10¹¹⁸(119-digit number)

15001259960742976277…84946539598658867839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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