Block #1,701,679

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/3/2016, 10:35:20 PM · Difficulty 10.6702 · 5,137,512 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d094118396e7a1f72578b33c5d86e7b4234998c0d33babbe718ee3dcc650965e

View on Chainz ↗

Height

#1,701,679

Difficulty

10.670178

Transactions

Size

572 B

Version

Bits

0aab90cd

Nonce

2,034,901,791

Timestamp

8/3/2016, 10:35:20 PM

Confirmations

5,137,512

Mined by

⛏️ TAUrSUXcCMztrsTBmWzc61dGaq6xjBGx7X9

Merkle Root

6fa95302b2e53163f4890664c8a59307fd3d51a484c47ef4e103c2429957e66b

Transactions (2)

Coinbase7d7b3e694bcbf8…977347d048faad

1 in → 1 out8.7800 XPM109 B

AUrSUXcC…xjBGx7X9

2fe286d0b5e80f…46c731406391c7

2 in → 2 out1.2164 XPM373 B

AKaaJEdY…BBsBWW4S AMx8Esnt…97T9RVgd

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.

1.712 × 10⁹⁴(95-digit number)

17125657959572095648…68082874169907071039

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

1.712 × 10⁹⁴(95-digit number)

17125657959572095648…68082874169907071039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.712 × 10⁹⁴(95-digit number)

17125657959572095648…68082874169907071041

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

3.425 × 10⁹⁴(95-digit number)

34251315919144191297…36165748339814142079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.425 × 10⁹⁴(95-digit number)

34251315919144191297…36165748339814142081

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

6.850 × 10⁹⁴(95-digit number)

68502631838288382595…72331496679628284159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.850 × 10⁹⁴(95-digit number)

68502631838288382595…72331496679628284161

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

1.370 × 10⁹⁵(96-digit number)

13700526367657676519…44662993359256568319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.370 × 10⁹⁵(96-digit number)

13700526367657676519…44662993359256568321

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

2.740 × 10⁹⁵(96-digit number)

27401052735315353038…89325986718513136639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.740 × 10⁹⁵(96-digit number)

27401052735315353038…89325986718513136641

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 #1,701,679

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