Block #66,413

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 5:18:58 PM · Difficulty 8.9861 · 6,723,527 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9100c91987cce397bc46f181a93a5999b43434c1db04182d044b8e102388577e

View on Chainz ↗

Height

#66,413

Difficulty

8.986136

Transactions

Size

202 B

Version

Bits

08fc7364

Nonce

329

Timestamp

7/19/2013, 5:18:58 PM

Confirmations

6,723,527

Merkle Root

1cc1b32fe7fdb6e85669169464f12c4fb43cd54abf7dd95bfd5b3f879e98caf9

Transactions (1)

Coinbase1cc1b32fe7fdb6…5b3f879e98caf9

1 in → 1 out12.3700 XPM110 B

AK1JUKWL…oPR4rN5o

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.

9.005 × 10⁹⁹(100-digit number)

90055891855352170270…50875851899484082879

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

9.005 × 10⁹⁹(100-digit number)

90055891855352170270…50875851899484082879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.005 × 10⁹⁹(100-digit number)

90055891855352170270…50875851899484082881

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

1.801 × 10¹⁰⁰(101-digit number)

18011178371070434054…01751703798968165759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.801 × 10¹⁰⁰(101-digit number)

18011178371070434054…01751703798968165761

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

3.602 × 10¹⁰⁰(101-digit number)

36022356742140868108…03503407597936331519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.602 × 10¹⁰⁰(101-digit number)

36022356742140868108…03503407597936331521

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

7.204 × 10¹⁰⁰(101-digit number)

72044713484281736216…07006815195872663039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.204 × 10¹⁰⁰(101-digit number)

72044713484281736216…07006815195872663041

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

1.440 × 10¹⁰¹(102-digit number)

14408942696856347243…14013630391745326079

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