Block #88,593

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/29/2013, 6:10:10 PM · Difficulty 9.2651 · 6,719,764 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7a9a4028572aee1696ae25598351f0c8b284860fc88cefbc63dc28393154722d

View on Chainz ↗

Height

#88,593

Difficulty

9.265137

Transactions

Size

504 B

Version

Bits

0943e00c

Nonce

77,213

Timestamp

7/29/2013, 6:10:10 PM

Confirmations

6,719,764

Mined by

⛏️ P2SHAMRJBb3V94CDPb3SssTj1B2eiHZv15uY6D

Merkle Root

ab7f7e9e359cd1c62ff3f2a26c7b79d74d255af9ffaf63c5c7919a9a241bdd9b

Transactions (2)

Coinbasefb8494cd7a383f…674f7779fdb6dc

1 in → 1 out11.6400 XPM109 B

AMRJBb3V…Zv15uY6D

4031aedef9f10d…dba05799b5382d

2 in → 1 out34.8100 XPM306 B

AWvvyEJH…DAk9m4bZ

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.

1.059 × 10⁹²(93-digit number)

10595980197298864482…06308382595072017859

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

1.059 × 10⁹²(93-digit number)

10595980197298864482…06308382595072017859

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.059 × 10⁹²(93-digit number)

10595980197298864482…06308382595072017861

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

2.119 × 10⁹²(93-digit number)

21191960394597728965…12616765190144035719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.119 × 10⁹²(93-digit number)

21191960394597728965…12616765190144035721

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

4.238 × 10⁹²(93-digit number)

42383920789195457931…25233530380288071439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.238 × 10⁹²(93-digit number)

42383920789195457931…25233530380288071441

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

8.476 × 10⁹²(93-digit number)

84767841578390915862…50467060760576142879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.476 × 10⁹²(93-digit number)

84767841578390915862…50467060760576142881

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

1.695 × 10⁹³(94-digit number)

16953568315678183172…00934121521152285759

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

Block #88,593

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