Block #30,982

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 9:30:36 PM · Difficulty 7.9879 · 6,777,729 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d3f8e003b28804ff553f5a5d0b1820858816e528b7b4b23e76d0136f5a535a75

View on Chainz ↗

Height

#30,982

Difficulty

7.987889

Transactions

Size

200 B

Version

Bits

07fce646

Nonce

112

Timestamp

7/13/2013, 9:30:36 PM

Confirmations

6,777,729

Mined by

⛏️ P2SHAWdtCUuJmNjYuej2P6C7RA2SGtHscHZriH

Merkle Root

2b1f6e5efeb7c961a1708b3e4a17129497ff6c244dee260c90f0a941095047ed

Transactions (1)

Coinbase2b1f6e5efeb7c9…f0a941095047ed

1 in → 1 out15.6500 XPM108 B

AWdtCUuJ…HscHZriH

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.

3.689 × 10⁹⁹(100-digit number)

36890448627326881592…99903338785631730819

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

3.689 × 10⁹⁹(100-digit number)

36890448627326881592…99903338785631730819

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.689 × 10⁹⁹(100-digit number)

36890448627326881592…99903338785631730821

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

7.378 × 10⁹⁹(100-digit number)

73780897254653763184…99806677571263461639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.378 × 10⁹⁹(100-digit number)

73780897254653763184…99806677571263461641

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

1.475 × 10¹⁰⁰(101-digit number)

14756179450930752636…99613355142526923279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.475 × 10¹⁰⁰(101-digit number)

14756179450930752636…99613355142526923281

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

2.951 × 10¹⁰⁰(101-digit number)

29512358901861505273…99226710285053846559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.951 × 10¹⁰⁰(101-digit number)

29512358901861505273…99226710285053846561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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 #30,982

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