Block #1,287,821

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/18/2015, 9:02:38 PM · Difficulty 10.8356 · 5,521,801 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

64b63f1be91f2242467271491609b9e5ae769aede35b1a0beb2182dea2403d20

View on Chainz ↗

Height

#1,287,821

Difficulty

10.835579

Transactions

Size

1.62 KB

Version

Bits

0ad5e889

Nonce

1,929,218,145

Timestamp

10/18/2015, 9:02:38 PM

Confirmations

5,521,801

Mined by

⛏️ P2SHAaa5ozgpskfcndazpgJnHnzoEQsQCpNMQJ

Merkle Root

49695b5f05335da4034706e94cef9f4ce498a384cb8423ef579ab3aed2cd2e3a

Transactions (4)

Coinbasea981a8661f327c…cf0fe9c9ef2976

1 in → 1 out8.5400 XPM110 B

Aaa5ozgp…sQCpNMQJ

cadbf077c37ea2…fbc1a9d0bd3148

1 in → 25 out170.7562 XPM1008 B

AeYTnBCP…iXZFJy4G ANprjeNE…E3RUWwhv AVMnST1q…tsJwuX6G ATuEdyaW…442tG6UG AYy3zv5s…kWnTQV8N

d8c3ced884284e…c32caa02089467

1 in → 2 out7.2936 XPM226 B

ARh4RYNx…cSZYSwGp AcuM7XiJ…5uND8Jce

346241fbb5f9a9…cc771f4c309f09

1 in → 2 out3.9478 XPM226 B

AGpa1gNF…rp6Duap3 AdqWXbiB…GTi1p6x9

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.

1.559 × 10⁹⁸(99-digit number)

15596546099539679019…01688605213312942079

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

1.559 × 10⁹⁸(99-digit number)

15596546099539679019…01688605213312942079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.559 × 10⁹⁸(99-digit number)

15596546099539679019…01688605213312942081

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

3.119 × 10⁹⁸(99-digit number)

31193092199079358038…03377210426625884159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.119 × 10⁹⁸(99-digit number)

31193092199079358038…03377210426625884161

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

6.238 × 10⁹⁸(99-digit number)

62386184398158716077…06754420853251768319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.238 × 10⁹⁸(99-digit number)

62386184398158716077…06754420853251768321

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

1.247 × 10⁹⁹(100-digit number)

12477236879631743215…13508841706503536639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.247 × 10⁹⁹(100-digit number)

12477236879631743215…13508841706503536641

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

2.495 × 10⁹⁹(100-digit number)

24954473759263486431…27017683413007073279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.495 × 10⁹⁹(100-digit number)

24954473759263486431…27017683413007073281

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 #1,287,821

Cookie Preferences