Block #30,709

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 8:19:36 PM · Difficulty 7.9874 · 6,775,260 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6597bcf5336d69ca9f2bb4bbd1346d012cafaa63e3ab03567fbe3a0436d62197

View on Chainz ↗

Height

#30,709

Difficulty

7.987383

Transactions

Size

203 B

Version

Bits

07fcc51e

Nonce

1,613

Timestamp

7/13/2013, 8:19:36 PM

Confirmations

6,775,260

Mined by

⛏️ P2SHAWdtCUuJmNjYuej2P6C7RA2SGtHscHZriH

Merkle Root

712f37dbaa65c0748c4291dec705ef9d37d23f7035889b398b4644a8bcc4cf16

Transactions (1)

Coinbase712f37dbaa65c0…4644a8bcc4cf16

1 in → 1 out15.6500 XPM109 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.

1.405 × 10¹⁰³(104-digit number)

14058887711942880689…19088098509586741759

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

1.405 × 10¹⁰³(104-digit number)

14058887711942880689…19088098509586741759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.405 × 10¹⁰³(104-digit number)

14058887711942880689…19088098509586741761

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

2.811 × 10¹⁰³(104-digit number)

28117775423885761379…38176197019173483519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.811 × 10¹⁰³(104-digit number)

28117775423885761379…38176197019173483521

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

5.623 × 10¹⁰³(104-digit number)

56235550847771522758…76352394038346967039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.623 × 10¹⁰³(104-digit number)

56235550847771522758…76352394038346967041

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

1.124 × 10¹⁰⁴(105-digit number)

11247110169554304551…52704788076693934079

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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