Block #3,335,171

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/31/2019, 5:05:23 PM · Difficulty 11.0011 · 3,505,590 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9a3e842f2e9a47d4d0c0edee6ad91f55975548c27c6e0e91864248246230cc3f

View on Chainz ↗

Height

#3,335,171

Difficulty

11.001120

Transactions

Size

575 B

Version

Bits

0b00496e

Nonce

1,276,064,507

Timestamp

8/31/2019, 5:05:23 PM

Confirmations

3,505,590

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

6ec2affb8c5e0b3f390353802d4cec9b65df8b60b2c3d2f1e0a01e754019f533

Transactions (2)

Coinbase2687d64a68d29f…70a2a4330c38e3

1 in → 1 out8.2600 XPM110 B

ASiq2qtK…VMhmk7yL

30ceb40f24a633…39b3ed8c4230f7

2 in → 2 out59.4184 XPM374 B

ANkkLLes…CEJqMsJZ ATQTf3Hn…a2K66k8V

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.

1.034 × 10⁹⁶(97-digit number)

10343045499807395448…89633184829583093759

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

1.034 × 10⁹⁶(97-digit number)

10343045499807395448…89633184829583093759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.034 × 10⁹⁶(97-digit number)

10343045499807395448…89633184829583093761

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

2.068 × 10⁹⁶(97-digit number)

20686090999614790897…79266369659166187519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.068 × 10⁹⁶(97-digit number)

20686090999614790897…79266369659166187521

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

4.137 × 10⁹⁶(97-digit number)

41372181999229581795…58532739318332375039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.137 × 10⁹⁶(97-digit number)

41372181999229581795…58532739318332375041

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

8.274 × 10⁹⁶(97-digit number)

82744363998459163590…17065478636664750079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.274 × 10⁹⁶(97-digit number)

82744363998459163590…17065478636664750081

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

1.654 × 10⁹⁷(98-digit number)

16548872799691832718…34130957273329500159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.654 × 10⁹⁷(98-digit number)

16548872799691832718…34130957273329500161

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

3.309 × 10⁹⁷(98-digit number)

33097745599383665436…68261914546659000319

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 #3,335,171

Cookie Preferences