Block #185,846

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/29/2013, 1:40:54 PM · Difficulty 9.8633 · 6,630,957 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a305c5b9955a5fe85d27e7276e0b3a25a16ee52272448ac8e1abe772d79a5ca5

View on Chainz ↗

Height

#185,846

Difficulty

9.863306

Transactions

Size

1.07 KB

Version

Bits

09dd01a7

Nonce

61,739

Timestamp

9/29/2013, 1:40:54 PM

Confirmations

6,630,957

Mined by

⛏️ P2SHAcasUkEWpybpa4fvEZjKikotiPoXR4wtHV

Merkle Root

f49d484e1156bd9cf5ab44dc4e446d93aec155559fcef871ad5009d6a669c02a

Transactions (3)

Coinbase58936e669eaca5…7c41f7ace9ebce

1 in → 1 out10.2900 XPM109 B

AcasUkEW…oXR4wtHV

4813d202560548…bcd061df3e4ccc

1 in → 2 out5.2499 XPM227 B

AUJScAEJ…4vf25tA3 AWmRJr7S…dPjuqZPd

031dfb93ca2fb6…2e07c19498249a

4 in → 2 out4.0435 XPM671 B

ARC34c2B…XiBBrx4X ASR2wMUA…G8qQUuwk

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.

1.336 × 10¹⁰¹(102-digit number)

13366023195033841154…63971701301431613439

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

1.336 × 10¹⁰¹(102-digit number)

13366023195033841154…63971701301431613439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.336 × 10¹⁰¹(102-digit number)

13366023195033841154…63971701301431613441

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

2.673 × 10¹⁰¹(102-digit number)

26732046390067682308…27943402602863226879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.673 × 10¹⁰¹(102-digit number)

26732046390067682308…27943402602863226881

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

5.346 × 10¹⁰¹(102-digit number)

53464092780135364617…55886805205726453759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.346 × 10¹⁰¹(102-digit number)

53464092780135364617…55886805205726453761

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

1.069 × 10¹⁰²(103-digit number)

10692818556027072923…11773610411452907519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.069 × 10¹⁰²(103-digit number)

10692818556027072923…11773610411452907521

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

2.138 × 10¹⁰²(103-digit number)

21385637112054145846…23547220822905815039

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 #185,846

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