Block #536,124

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/11/2014, 7:05:03 AM · Difficulty 10.9077 · 6,269,552 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

275523063326bd3999dff0a07db0cc32176f2e6a8f79e4325077f75c9708fa97

View on Chainz ↗

Height

#536,124

Difficulty

10.907656

Transactions

Size

697 B

Version

Bits

0ae85c2b

Nonce

69,389

Timestamp

5/11/2014, 7:05:03 AM

Confirmations

6,269,552

Mined by

⛏️ <.aSo!AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

477477a6bd7366ac99f3784411b74d021928384c47d4bd5b03ebbc053040d437

Transactions (1)

Coinbase477477a6bd7366…ebbc053040d437

1 in → 16 out8.3889 XPM607 B

AQvZBsUo…hppgRZTJ AdxPNkWD…ZMa9u34q AUbecsVa…i8zo8qRf AJtNW28X…Syb4Ph5j ATKK7iFz…wZm46KN1

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.

9.166 × 10⁹³(94-digit number)

91661877826946239382…89713463065084513279

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

9.166 × 10⁹³(94-digit number)

91661877826946239382…89713463065084513279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.166 × 10⁹³(94-digit number)

91661877826946239382…89713463065084513281

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

1.833 × 10⁹⁴(95-digit number)

18332375565389247876…79426926130169026559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.833 × 10⁹⁴(95-digit number)

18332375565389247876…79426926130169026561

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

3.666 × 10⁹⁴(95-digit number)

36664751130778495753…58853852260338053119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.666 × 10⁹⁴(95-digit number)

36664751130778495753…58853852260338053121

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

7.332 × 10⁹⁴(95-digit number)

73329502261556991506…17707704520676106239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.332 × 10⁹⁴(95-digit number)

73329502261556991506…17707704520676106241

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

1.466 × 10⁹⁵(96-digit number)

14665900452311398301…35415409041352212479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.466 × 10⁹⁵(96-digit number)

14665900452311398301…35415409041352212481

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