Block #75,662

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 5:56:09 PM · Difficulty 9.0288 · 6,723,712 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e3ccd68b986940f906e1213d1336e9b300141e4757d6ea68d94c3d9b8e910d5b

View on Chainz ↗

Height

#75,662

Difficulty

9.028791

Transactions

Size

202 B

Version

Bits

09075edc

Nonce

117

Timestamp

7/21/2013, 5:56:09 PM

Confirmations

6,723,712

Mined by

⛏️ P2SHAawzRYLpHU7wZxoYUFawXzGZd4NJSmHiTJ

Merkle Root

029514666c3e5feeb6bf946c75292cf53e7a9ee8860ff19ef54422a412ca0c5a

Transactions (1)

Coinbase029514666c3e5f…4422a412ca0c5a

1 in → 1 out12.2500 XPM110 B

AawzRYLp…NJSmHiTJ

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.

1.312 × 10⁹⁹(100-digit number)

13122287975128035982…52069709383386899949

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

1.312 × 10⁹⁹(100-digit number)

13122287975128035982…52069709383386899949

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.312 × 10⁹⁹(100-digit number)

13122287975128035982…52069709383386899951

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

2.624 × 10⁹⁹(100-digit number)

26244575950256071964…04139418766773799899

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.624 × 10⁹⁹(100-digit number)

26244575950256071964…04139418766773799901

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

5.248 × 10⁹⁹(100-digit number)

52489151900512143928…08278837533547599799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.248 × 10⁹⁹(100-digit number)

52489151900512143928…08278837533547599801

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

1.049 × 10¹⁰⁰(101-digit number)

10497830380102428785…16557675067095199599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.049 × 10¹⁰⁰(101-digit number)

10497830380102428785…16557675067095199601

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

2.099 × 10¹⁰⁰(101-digit number)

20995660760204857571…33115350134190399199

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