Block #75,087

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 2:33:55 PM · Difficulty 8.9959 · 6,714,773 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5225a6b16df23915bd5a22290a5e1afeefb850ba40b00d0cddc43b36bdaa74fa

View on Chainz ↗

Height

#75,087

Difficulty

8.995903

Transactions

Size

205 B

Version

Bits

08fef37f

Nonce

417

Timestamp

7/21/2013, 2:33:55 PM

Confirmations

6,714,773

Merkle Root

5bed33411c620bda62d9d4a9be119a210339c594a88c8254e743a56021f8c24a

Transactions (1)

Coinbase5bed33411c620b…43a56021f8c24a

1 in → 1 out12.3400 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.

2.237 × 10¹⁰⁷(108-digit number)

22374352167398751848…21526791845067422159

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

2.237 × 10¹⁰⁷(108-digit number)

22374352167398751848…21526791845067422159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.237 × 10¹⁰⁷(108-digit number)

22374352167398751848…21526791845067422161

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

4.474 × 10¹⁰⁷(108-digit number)

44748704334797503697…43053583690134844319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.474 × 10¹⁰⁷(108-digit number)

44748704334797503697…43053583690134844321

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

8.949 × 10¹⁰⁷(108-digit number)

89497408669595007395…86107167380269688639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.949 × 10¹⁰⁷(108-digit number)

89497408669595007395…86107167380269688641

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

1.789 × 10¹⁰⁸(109-digit number)

17899481733919001479…72214334760539377279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.789 × 10¹⁰⁸(109-digit number)

17899481733919001479…72214334760539377281

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

3.579 × 10¹⁰⁸(109-digit number)

35798963467838002958…44428669521078754559

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