Block #3,250,435

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/2/2019, 1:45:14 PM · Difficulty 11.0015 · 3,591,342 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

70b466a3f13450ee84d964a7d09dace412ceac374cff91a6ee4da6a86f279b37

View on Chainz ↗

Height

#3,250,435

Difficulty

11.001516

Transactions

Size

67.07 KB

Version

Bits

0b006359

Nonce

1,367,713,794

Timestamp

7/2/2019, 1:45:14 PM

Confirmations

3,591,342

Mined by

⛏️ P2SHAMS4NKJwrZbcDiYBsc5zTFEMPHsVYNTVNh

Merkle Root

a72612bf2f1e8f74d7401bd191c26355c9f5a4c6f729eb212af88ac493c6ecd1

Transactions (2)

Coinbased65ef0601eeea8…a1b2bbdc48c180

1 in → 1 out8.9400 XPM109 B

AMS4NKJw…sVYNTVNh

e19d83019d3a0f…9c07bfc0b1ad58

600 in → 2 out4954.4100 XPM66.87 KB

AFybbP2J…hk38SED1 AKz3ReFF…PLJFgKHd

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.

3.290 × 10⁹⁶(97-digit number)

32905397886257733099…79273497116901006079

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

3.290 × 10⁹⁶(97-digit number)

32905397886257733099…79273497116901006079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.290 × 10⁹⁶(97-digit number)

32905397886257733099…79273497116901006081

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

6.581 × 10⁹⁶(97-digit number)

65810795772515466199…58546994233802012159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.581 × 10⁹⁶(97-digit number)

65810795772515466199…58546994233802012161

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

1.316 × 10⁹⁷(98-digit number)

13162159154503093239…17093988467604024319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.316 × 10⁹⁷(98-digit number)

13162159154503093239…17093988467604024321

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

2.632 × 10⁹⁷(98-digit number)

26324318309006186479…34187976935208048639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.632 × 10⁹⁷(98-digit number)

26324318309006186479…34187976935208048641

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

5.264 × 10⁹⁷(98-digit number)

52648636618012372959…68375953870416097279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.264 × 10⁹⁷(98-digit number)

52648636618012372959…68375953870416097281

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

1.052 × 10⁹⁸(99-digit number)

10529727323602474591…36751907740832194559

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 #3,250,435

Cookie Preferences