Block #537,158

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/11/2014, 5:51:19 PM · Difficulty 10.9146 · 6,273,816 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

99c607acc89c294f253ac32ac6c0616873d1d81ab3b887ace237b2e6e95d5dc1

View on Chainz ↗

Height

#537,158

Difficulty

10.914566

Transactions

Size

731 B

Version

Bits

0aea20ff

Nonce

261,887

Timestamp

5/11/2014, 5:51:19 PM

Confirmations

6,273,816

Mined by

⛏️ F2aSoAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

6be7c7d4ba0613ad4c487480aa7a83a0abfa58f5aebc21c26667bf0c32769567

Transactions (1)

Coinbase6be7c7d4ba0613…67bf0c32769567

1 in → 17 out8.3800 XPM641 B

AQvZBsUo…hppgRZTJ AdxPNkWD…ZMa9u34q AUbecsVa…i8zo8qRf AJtNW28X…Syb4Ph5j AQyr8Lw3…hs4nt3Pn

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.

2.014 × 10⁹⁵(96-digit number)

20147578001844627865…98396365601319802239

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

2.014 × 10⁹⁵(96-digit number)

20147578001844627865…98396365601319802239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.014 × 10⁹⁵(96-digit number)

20147578001844627865…98396365601319802241

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

4.029 × 10⁹⁵(96-digit number)

40295156003689255730…96792731202639604479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.029 × 10⁹⁵(96-digit number)

40295156003689255730…96792731202639604481

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

8.059 × 10⁹⁵(96-digit number)

80590312007378511460…93585462405279208959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.059 × 10⁹⁵(96-digit number)

80590312007378511460…93585462405279208961

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

1.611 × 10⁹⁶(97-digit number)

16118062401475702292…87170924810558417919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.611 × 10⁹⁶(97-digit number)

16118062401475702292…87170924810558417921

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

3.223 × 10⁹⁶(97-digit number)

32236124802951404584…74341849621116835839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.223 × 10⁹⁶(97-digit number)

32236124802951404584…74341849621116835841

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 #537,158

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