Block #87,266

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/28/2013, 6:37:33 PM · Difficulty 9.2776 · 6,715,461 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

50ed89c2f5d97502a3e61031ac97bd0aac2297e00f1400ae40b2b9a49a6c76aa

View on Chainz ↗

Height

#87,266

Difficulty

9.277582

Transactions

Size

579 B

Version

Bits

09470f9d

Nonce

758,912

Timestamp

7/28/2013, 6:37:33 PM

Confirmations

6,715,461

Mined by

⛏️ P2SHAUHe9qSvkLPrbHQ2y97nzDwxnwYe4ZG3SP

Merkle Root

33e35b76126dd41a1ed255706b4b08911231993858ca82076f952252945f45d3

Transactions (2)

Coinbase9966617fbce0a2…7feb1d5a2ce441

1 in → 1 out11.6100 XPM109 B

AUHe9qSv…Ye4ZG3SP

b802ce844375f0…bf3c49f677c2a3

2 in → 2 out100.2183 XPM375 B

AXpdNesU…ZiMo5ZaZ AKZHGNpJ…FByhphHp

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.

1.500 × 10¹⁰⁷(108-digit number)

15002167276812190784…89488010346969210119

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

1.500 × 10¹⁰⁷(108-digit number)

15002167276812190784…89488010346969210119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.500 × 10¹⁰⁷(108-digit number)

15002167276812190784…89488010346969210121

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

3.000 × 10¹⁰⁷(108-digit number)

30004334553624381568…78976020693938420239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.000 × 10¹⁰⁷(108-digit number)

30004334553624381568…78976020693938420241

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

6.000 × 10¹⁰⁷(108-digit number)

60008669107248763136…57952041387876840479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.000 × 10¹⁰⁷(108-digit number)

60008669107248763136…57952041387876840481

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

1.200 × 10¹⁰⁸(109-digit number)

12001733821449752627…15904082775753680959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.200 × 10¹⁰⁸(109-digit number)

12001733821449752627…15904082775753680961

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

2.400 × 10¹⁰⁸(109-digit number)

24003467642899505254…31808165551507361919

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