Block #286,812

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/1/2013, 1:16:09 AM · Difficulty 9.9860 · 6,505,107 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7b79d9ee2acd87711874f184339523f36d94ccc223eb7502d3ba3696bbac104a

View on Chainz ↗

Height

#286,812

Difficulty

9.986040

Transactions

Size

1.01 KB

Version

Bits

09fc6d1c

Nonce

178,925

Timestamp

12/1/2013, 1:16:09 AM

Confirmations

6,505,107

Merkle Root

459f363ca35ed4d98fd92a10b84826426a0d65696b45f8ff22b2d89a5dc87cf3

Transactions (1)

Coinbase459f363ca35ed4…b2d89a5dc87cf3

1 in → 26 out10.0097 XPM947 B

Ac735H3b…msgiCGB8 AdV5u966…MgezYDKc AYcLTeXR…bscgPops AQwRN8bE…V8PsTcY9 ALw8WzMm…sj2uYfgL

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.

6.153 × 10⁹⁶(97-digit number)

61536199344362212044…83503650402319334399

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

6.153 × 10⁹⁶(97-digit number)

61536199344362212044…83503650402319334399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.153 × 10⁹⁶(97-digit number)

61536199344362212044…83503650402319334401

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

1.230 × 10⁹⁷(98-digit number)

12307239868872442408…67007300804638668799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.230 × 10⁹⁷(98-digit number)

12307239868872442408…67007300804638668801

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

2.461 × 10⁹⁷(98-digit number)

24614479737744884817…34014601609277337599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.461 × 10⁹⁷(98-digit number)

24614479737744884817…34014601609277337601

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

4.922 × 10⁹⁷(98-digit number)

49228959475489769635…68029203218554675199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.922 × 10⁹⁷(98-digit number)

49228959475489769635…68029203218554675201

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

9.845 × 10⁹⁷(98-digit number)

98457918950979539270…36058406437109350399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.845 × 10⁹⁷(98-digit number)

98457918950979539270…36058406437109350401

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