Block #538,363

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/12/2014, 7:13:05 AM · Difficulty 10.9211 · 6,306,566 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d2156776bf57a565684d2c04fdbdbc99df5c14fe89022b4c3a9638ea013e8eef

View on Chainz ↗

Height

#538,363

Difficulty

10.921134

Transactions

Size

885 B

Version

Bits

0aebcf71

Nonce

1,810,450

Timestamp

5/12/2014, 7:13:05 AM

Confirmations

6,306,566

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

3f0f6e972b3c4d67f1b39b6891d8431cbd964d9c5c3f4323ef03df975cbecfa1

Transactions (4)

Coinbase14c5b203038169…e069b68a80f907

1 in → 1 out8.4000 XPM116 B

ANSXnLY2…Sd25TjkD

a6f8e093157add…254996a1fc812b

1 in → 2 out6.8613 XPM226 B

AYxjdDKR…hHejoDQs ALk1dDaF…MzJgTD8i

e349a782968991…520d294f84db04

1 in → 2 out0.8125 XPM225 B

AYzKfhPL…Pf6t7Yip AHU3ZAYi…E4grhoYJ

def29329afd655…4defa211a14c94

1 in → 2 out6.2264 XPM226 B

AWGrEQQC…pZxhYH4m AcX2bxZa…HBkCQYsH

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.

3.115 × 10⁹⁸(99-digit number)

31153437633627322608…28954198966069132319

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

3.115 × 10⁹⁸(99-digit number)

31153437633627322608…28954198966069132319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.115 × 10⁹⁸(99-digit number)

31153437633627322608…28954198966069132321

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

6.230 × 10⁹⁸(99-digit number)

62306875267254645217…57908397932138264639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.230 × 10⁹⁸(99-digit number)

62306875267254645217…57908397932138264641

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

1.246 × 10⁹⁹(100-digit number)

12461375053450929043…15816795864276529279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.246 × 10⁹⁹(100-digit number)

12461375053450929043…15816795864276529281

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

2.492 × 10⁹⁹(100-digit number)

24922750106901858086…31633591728553058559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.492 × 10⁹⁹(100-digit number)

24922750106901858086…31633591728553058561

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

4.984 × 10⁹⁹(100-digit number)

49845500213803716173…63267183457106117119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.984 × 10⁹⁹(100-digit number)

49845500213803716173…63267183457106117121

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

Block #538,363

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