Block #73,241

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 4:48:16 AM · Difficulty 8.9947 · 6,718,177 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d46d14b119a49d91f744bf813357cf3d6f8f1eb6ee806238edcc7f11cc45787d

View on Chainz ↗

Height

#73,241

Difficulty

8.994677

Transactions

Size

202 B

Version

Bits

08fea323

Nonce

1,227

Timestamp

7/21/2013, 4:48:16 AM

Confirmations

6,718,177

Merkle Root

57d1072ba0071118040613dd50875841fe9053602ecf713886271a2356bcc1d2

Transactions (1)

Coinbase57d1072ba00711…271a2356bcc1d2

1 in → 1 out12.3400 XPM110 B

ANCYL9xh…9WyGnqDE

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.

7.153 × 10⁹⁹(100-digit number)

71532517502054591978…62363646876718999099

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

7.153 × 10⁹⁹(100-digit number)

71532517502054591978…62363646876718999099

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.153 × 10⁹⁹(100-digit number)

71532517502054591978…62363646876718999101

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

1.430 × 10¹⁰⁰(101-digit number)

14306503500410918395…24727293753437998199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.430 × 10¹⁰⁰(101-digit number)

14306503500410918395…24727293753437998201

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

2.861 × 10¹⁰⁰(101-digit number)

28613007000821836791…49454587506875996399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.861 × 10¹⁰⁰(101-digit number)

28613007000821836791…49454587506875996401

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

5.722 × 10¹⁰⁰(101-digit number)

57226014001643673582…98909175013751992799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.722 × 10¹⁰⁰(101-digit number)

57226014001643673582…98909175013751992801

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

1.144 × 10¹⁰¹(102-digit number)

11445202800328734716…97818350027503985599

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