Block #59,790

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 4:17:33 AM · Difficulty 8.9665 · 6,732,691 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3a03a9afa6fc857f4980c2630df66c210f294496ca574797451d35f126b89cec

View on Chainz ↗

Height

#59,790

Difficulty

8.966466

Transactions

Size

202 B

Version

Bits

08f76a51

Nonce

263

Timestamp

7/18/2013, 4:17:33 AM

Confirmations

6,732,691

Merkle Root

0211cb6917fad6ebe5051f74d503adb23ea7f9a9a5c004437f0f16f44f8e8669

Transactions (1)

Coinbase0211cb6917fad6…0f16f44f8e8669

1 in → 1 out12.4200 XPM110 B

AbVevYKa…Zd6sVfcp

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.

8.516 × 10⁹⁹(100-digit number)

85161979140793200296…71449279570255154219

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

8.516 × 10⁹⁹(100-digit number)

85161979140793200296…71449279570255154219

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.516 × 10⁹⁹(100-digit number)

85161979140793200296…71449279570255154221

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

1.703 × 10¹⁰⁰(101-digit number)

17032395828158640059…42898559140510308439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.703 × 10¹⁰⁰(101-digit number)

17032395828158640059…42898559140510308441

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

3.406 × 10¹⁰⁰(101-digit number)

34064791656317280118…85797118281020616879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.406 × 10¹⁰⁰(101-digit number)

34064791656317280118…85797118281020616881

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

6.812 × 10¹⁰⁰(101-digit number)

68129583312634560236…71594236562041233759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.812 × 10¹⁰⁰(101-digit number)

68129583312634560236…71594236562041233761

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

1.362 × 10¹⁰¹(102-digit number)

13625916662526912047…43188473124082467519

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