Block #2,269,634

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/27/2017, 2:05:50 AM · Difficulty 10.9525 · 4,570,117 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a5ea3ffa0afe126b1e2947d3b75010d40e35cb1fdb7a9b41807527310e550f22

View on Chainz ↗

Height

#2,269,634

Difficulty

10.952500

Transactions

Size

1.37 KB

Version

Bits

0af3d710

Nonce

1,024,787,511

Timestamp

8/27/2017, 2:05:50 AM

Confirmations

4,570,117

Mined by

⛏️ P2SHATFYdDGd2HYYp36iqM9HgJgDPXf7xXdDJk

Merkle Root

a5f4e605afb6c63faf1559a98adf1cc92264dcfd5c41a60adb838ae0936fcfe2

Transactions (5)

Coinbased739bc6574b87d…507d42d6e463eb

1 in → 1 out8.3600 XPM110 B

ATFYdDGd…f7xXdDJk

f543fccd0bd0bf…1cd30e754d4927

2 in → 2 out707.5881 XPM374 B

AGoBR7Ub…HPRkJb54 APCLwsZN…Y9nxkbdb

d534965c19c4d0…ea181ce85ec3bb

1 in → 2 out346.3115 XPM225 B

AKb4H2rk…ueRYQ5RX Adqg1A4p…Efz6WLU6

c7a14eb3e174ca…3d097c8af046b8

2 in → 2 out5.0335 XPM374 B

AMeEiv2y…G8LAXobW ASdXKexa…kch59HW5

5a035f340859f7…0383ace90224ad

1 in → 2 out2.2098 XPM227 B

AexXjs9T…JZgyxkZQ AQBd5saN…gzPybU6u

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.

4.280 × 10⁹³(94-digit number)

42800349350370679302…42613363468379155799

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

4.280 × 10⁹³(94-digit number)

42800349350370679302…42613363468379155799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.280 × 10⁹³(94-digit number)

42800349350370679302…42613363468379155801

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

8.560 × 10⁹³(94-digit number)

85600698700741358604…85226726936758311599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.560 × 10⁹³(94-digit number)

85600698700741358604…85226726936758311601

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

1.712 × 10⁹⁴(95-digit number)

17120139740148271720…70453453873516623199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.712 × 10⁹⁴(95-digit number)

17120139740148271720…70453453873516623201

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

3.424 × 10⁹⁴(95-digit number)

34240279480296543441…40906907747033246399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.424 × 10⁹⁴(95-digit number)

34240279480296543441…40906907747033246401

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

6.848 × 10⁹⁴(95-digit number)

68480558960593086883…81813815494066492799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.848 × 10⁹⁴(95-digit number)

68480558960593086883…81813815494066492801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.369 × 10⁹⁵(96-digit number)

13696111792118617376…63627630988132985599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,269,634

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