Block #252,769

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/9/2013, 6:27:07 PM · Difficulty 9.9715 · 6,563,819 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

916952c90c0a2d9075ba17dfb240772d7c546161ad88059e5931e2c5fb90057b

View on Chainz ↗

Height

#252,769

Difficulty

9.971515

Transactions

Size

683 B

Version

Bits

09f8b53a

Nonce

317,116

Timestamp

11/9/2013, 6:27:07 PM

Confirmations

6,563,819

Mined by

⛏️ P2SHAWd2mnipWMazuwYMoBoMoCPixQdvKr5Di1

Merkle Root

011bc886174640ae8e887f862b43dfc05289a7cac5372c244618f3c9b8fb5fec

Transactions (3)

Coinbasea8b3e7ac35a0b4…8b4820928e2d49

1 in → 1 out10.0600 XPM109 B

AWd2mnip…dvKr5Di1

7225291201b128…448f8bf15330cd

1 in → 4 out10.0400 XPM261 B

ALXnWdQE…BBQNdhFQ AeKNrjNj…1NEq95Ta AU8iJphA…H9jExtRV AUDB1fin…mSCsqMVN

01608f3949a138…15021cbce2c377

1 in → 2 out2.2220 XPM225 B

APBYNrbx…sdi7imsF AJKuZiw4…1Myb5ciP

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.

1.129 × 10⁹⁰(91-digit number)

11299379278476228470…63840616213508710399

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

1.129 × 10⁹⁰(91-digit number)

11299379278476228470…63840616213508710399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.129 × 10⁹⁰(91-digit number)

11299379278476228470…63840616213508710401

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

2.259 × 10⁹⁰(91-digit number)

22598758556952456940…27681232427017420799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.259 × 10⁹⁰(91-digit number)

22598758556952456940…27681232427017420801

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

4.519 × 10⁹⁰(91-digit number)

45197517113904913881…55362464854034841599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.519 × 10⁹⁰(91-digit number)

45197517113904913881…55362464854034841601

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

9.039 × 10⁹⁰(91-digit number)

90395034227809827762…10724929708069683199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.039 × 10⁹⁰(91-digit number)

90395034227809827762…10724929708069683201

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

1.807 × 10⁹¹(92-digit number)

18079006845561965552…21449859416139366399

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

Block #252,769

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