Block #253,745

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/10/2013, 8:04:58 AM · Difficulty 9.9724 · 6,578,133 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f65d26b93981a544f13194e1979345725dce9e6234e28f7b0fa40f23f462089d

View on Chainz ↗

Height

#253,745

Difficulty

9.972418

Transactions

Size

1.84 KB

Version

Bits

09f8f066

Nonce

47,460

Timestamp

11/10/2013, 8:04:58 AM

Confirmations

6,578,133

Mined by

⛏️ 1aR>CAaScufsRjcMXqEnB38BdpSxZe6uC5rkVai

Merkle Root

ace43894097b334a754b8cb24a8dcce7052b1e582ba0417c08259d99b678a84d

Transactions (1)

Coinbaseace43894097b33…259d99b678a84d

1 in → 51 out10.0200 XPM1.75 KB

AaScufsR…uC5rkVai AKXeSXzu…yeuNjvhB AScCYXya…oAz38X3p AKDTDDtx…iqvw9cdY AJzWx2VD…j4ZSMit5

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.

1.085 × 10⁹²(93-digit number)

10857769742933632186…54672905839234198719

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

1.085 × 10⁹²(93-digit number)

10857769742933632186…54672905839234198719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.085 × 10⁹²(93-digit number)

10857769742933632186…54672905839234198721

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

2.171 × 10⁹²(93-digit number)

21715539485867264372…09345811678468397439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.171 × 10⁹²(93-digit number)

21715539485867264372…09345811678468397441

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

4.343 × 10⁹²(93-digit number)

43431078971734528744…18691623356936794879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.343 × 10⁹²(93-digit number)

43431078971734528744…18691623356936794881

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

8.686 × 10⁹²(93-digit number)

86862157943469057489…37383246713873589759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.686 × 10⁹²(93-digit number)

86862157943469057489…37383246713873589761

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

1.737 × 10⁹³(94-digit number)

17372431588693811497…74766493427747179519

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 #253,745

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