Block #275,184

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 2:29:26 PM · Difficulty 9.9600 · 6,516,467 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

64f892f2895f2bfe3f4ca8a4bbf8fe76949f5e2e73105d5e3136c48d0b815807

View on Chainz ↗

Height

#275,184

Difficulty

9.960013

Transactions

Size

2.76 KB

Version

Bits

09f5c362

Nonce

5,012

Timestamp

11/26/2013, 2:29:26 PM

Confirmations

6,516,467

Merkle Root

f68bd7ca6e9da10330584532fc2e3b2c9323c149b1506a30f23cc63508a7737f

Transactions (2)

Coinbase4c3d8cb818f646…139f437fbc0359

1 in → 2 out10.1000 XPM141 B

AKcbk49N…GJbKa7j1 AKNbfPoc…jfkpwAyL

95524693d84748…627782cbd23509

17 in → 2 out161.3508 XPM2.53 KB

AeC7BJnb…wrzN68s7 ATYsfxuX…tmGDHG1E

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.

1.898 × 10¹⁰⁵(106-digit number)

18987821767398744986…74140789387377285119

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

1.898 × 10¹⁰⁵(106-digit number)

18987821767398744986…74140789387377285119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.898 × 10¹⁰⁵(106-digit number)

18987821767398744986…74140789387377285121

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

3.797 × 10¹⁰⁵(106-digit number)

37975643534797489973…48281578774754570239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.797 × 10¹⁰⁵(106-digit number)

37975643534797489973…48281578774754570241

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

7.595 × 10¹⁰⁵(106-digit number)

75951287069594979947…96563157549509140479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.595 × 10¹⁰⁵(106-digit number)

75951287069594979947…96563157549509140481

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

1.519 × 10¹⁰⁶(107-digit number)

15190257413918995989…93126315099018280959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.519 × 10¹⁰⁶(107-digit number)

15190257413918995989…93126315099018280961

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

3.038 × 10¹⁰⁶(107-digit number)

30380514827837991978…86252630198036561919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.038 × 10¹⁰⁶(107-digit number)

30380514827837991978…86252630198036561921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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