Block #231,139

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/28/2013, 6:12:42 AM · Difficulty 9.9404 · 6,565,308 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cf95b20c34de0187568398906177321958960c838fab3193915438d120e1fc7a

View on Chainz ↗

Height

#231,139

Difficulty

9.940351

Transactions

Size

423 B

Version

Bits

09f0bad4

Nonce

46,223

Timestamp

10/28/2013, 6:12:42 AM

Confirmations

6,565,308

Mined by

⛏️ P2SHAYc3QGYaSv1sA3FuuZuBoiE4ttSWDuszQp

Merkle Root

f6c93e549b18c367cdef5c3830c6c4ee01e279ced089fd19e91a3ccf1c990b67

Transactions (2)

Coinbaseadd11131a14578…dae38090220957

1 in → 1 out10.1200 XPM109 B

AYc3QGYa…SWDuszQp

01eeccf2a38bd5…c089d6486538a7

1 in → 2 out2.8623 XPM225 B

AbjLQB3Y…SXLCXwVY AJG7cQWZ…jTW6swhh

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.

1.920 × 10⁹²(93-digit number)

19209439753816165456…93265083439206535199

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

1.920 × 10⁹²(93-digit number)

19209439753816165456…93265083439206535199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.920 × 10⁹²(93-digit number)

19209439753816165456…93265083439206535201

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

3.841 × 10⁹²(93-digit number)

38418879507632330912…86530166878413070399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.841 × 10⁹²(93-digit number)

38418879507632330912…86530166878413070401

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

7.683 × 10⁹²(93-digit number)

76837759015264661825…73060333756826140799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.683 × 10⁹²(93-digit number)

76837759015264661825…73060333756826140801

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

1.536 × 10⁹³(94-digit number)

15367551803052932365…46120667513652281599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.536 × 10⁹³(94-digit number)

15367551803052932365…46120667513652281601

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

3.073 × 10⁹³(94-digit number)

30735103606105864730…92241335027304563199

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