Block #33,487

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 4:57:16 AM · Difficulty 7.9920 · 6,782,370 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

851ca5372372f8c178494efdc8bb348093e66281c9ce48fac4a0c93a783c43cd

View on Chainz ↗

Height

#33,487

Difficulty

7.992008

Transactions

Size

198 B

Version

Bits

07fdf43b

Nonce

594

Timestamp

7/14/2013, 4:57:16 AM

Confirmations

6,782,370

Mined by

⛏️ P2SHALXjrugCYbt29xU2ER2ywowb9GhByoynjy

Merkle Root

d12e18233da7516fe5863194907e637183c6ca8906660d283f50ce904ce7c807

Transactions (1)

Coinbased12e18233da751…50ce904ce7c807

1 in → 1 out15.6400 XPM109 B

ALXjrugC…hByoynjy

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.

2.112 × 10⁹³(94-digit number)

21126384452413573641…13958814214478071799

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

2.112 × 10⁹³(94-digit number)

21126384452413573641…13958814214478071799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.112 × 10⁹³(94-digit number)

21126384452413573641…13958814214478071801

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

4.225 × 10⁹³(94-digit number)

42252768904827147282…27917628428956143599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.225 × 10⁹³(94-digit number)

42252768904827147282…27917628428956143601

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

8.450 × 10⁹³(94-digit number)

84505537809654294565…55835256857912287199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.450 × 10⁹³(94-digit number)

84505537809654294565…55835256857912287201

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

1.690 × 10⁹⁴(95-digit number)

16901107561930858913…11670513715824574399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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

Block #33,487

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