Block #2,052,674

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/3/2017, 10:22:04 PM · Difficulty 10.7491 · 4,790,141 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

50a1e4850f6df22a695ca7fcc6868f0b44259d182806ebcb7201191431437a08

View on Chainz ↗

Height

#2,052,674

Difficulty

10.749114

Transactions

Size

1.70 KB

Version

Bits

0abfc5ea

Nonce

94,736,680

Timestamp

4/3/2017, 10:22:04 PM

Confirmations

4,790,141

Mined by

⛏️ P2SHAPJj2iUafZt9jFfbYUzAcuh4CttHm5idfW

Merkle Root

d4a6d249f1b5c65f9adcea04394d1448b845dbbcc9b3c30a867717ae7431cecc

Transactions (4)

Coinbaseb40fc290e31c1b…d8c6b48e5cea0c

1 in → 1 out8.6800 XPM110 B

APJj2iUa…tHm5idfW

fe26f40a698972…cd897c91eef027

6 in → 2 out16.2800 XPM935 B

AbxbAUaL…uX3gA9SK AWrHsGnT…QJxpuadi

a4f0d7b5a71f7a…a3e791f51ade2f

1 in → 2 out4.3600 XPM226 B

AcYpTxGL…GfeLPQRa AJsdRJpQ…8kNJyuhP

9cee274d6d196e…968b3f18635d3d

2 in → 2 out1.0700 XPM374 B

AREqBK4E…chtFqsdb AcHcmYhF…pSZeqRRb

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.

5.174 × 10⁹⁷(98-digit number)

51742221755195798591…89967199087204270079

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

5.174 × 10⁹⁷(98-digit number)

51742221755195798591…89967199087204270079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.174 × 10⁹⁷(98-digit number)

51742221755195798591…89967199087204270081

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

1.034 × 10⁹⁸(99-digit number)

10348444351039159718…79934398174408540159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.034 × 10⁹⁸(99-digit number)

10348444351039159718…79934398174408540161

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

2.069 × 10⁹⁸(99-digit number)

20696888702078319436…59868796348817080319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.069 × 10⁹⁸(99-digit number)

20696888702078319436…59868796348817080321

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

4.139 × 10⁹⁸(99-digit number)

41393777404156638873…19737592697634160639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.139 × 10⁹⁸(99-digit number)

41393777404156638873…19737592697634160641

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

8.278 × 10⁹⁸(99-digit number)

82787554808313277746…39475185395268321279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.278 × 10⁹⁸(99-digit number)

82787554808313277746…39475185395268321281

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 #2,052,674

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