Block #81,473

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/24/2013, 6:55:12 PM · Difficulty 9.2699 · 6,708,278 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c2b96b372e0fa7cf4623741d819534d5a3b2d2313da89d386cfd31b747b06729

View on Chainz ↗

Height

#81,473

Difficulty

9.269934

Transactions

Size

580 B

Version

Bits

09451a5d

Nonce

133

Timestamp

7/24/2013, 6:55:12 PM

Confirmations

6,708,278

Merkle Root

aa731555ed6811d77760e3c99d341fce0d52dba04cc1ea9a936f3621ceee9e2e

Transactions (2)

Coinbase548405cded5143…1e91338dd9bfa1

1 in → 1 out11.6300 XPM110 B

Aaa5Cngt…udV1fbB3

7418053b79e3a1…85e4adf378e78e

2 in → 2 out42.7673 XPM375 B

Abj37aSM…JdMQyRPY Ad1jCp91…wnnuA449

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.

1.462 × 10¹⁰⁷(108-digit number)

14628677856610598445…91504955744512989999

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

1.462 × 10¹⁰⁷(108-digit number)

14628677856610598445…91504955744512989999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.462 × 10¹⁰⁷(108-digit number)

14628677856610598445…91504955744512990001

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

2.925 × 10¹⁰⁷(108-digit number)

29257355713221196891…83009911489025979999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.925 × 10¹⁰⁷(108-digit number)

29257355713221196891…83009911489025980001

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

5.851 × 10¹⁰⁷(108-digit number)

58514711426442393783…66019822978051959999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.851 × 10¹⁰⁷(108-digit number)

58514711426442393783…66019822978051960001

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

1.170 × 10¹⁰⁸(109-digit number)

11702942285288478756…32039645956103919999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.170 × 10¹⁰⁸(109-digit number)

11702942285288478756…32039645956103920001

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

2.340 × 10¹⁰⁸(109-digit number)

23405884570576957513…64079291912207839999

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