Block #2,170,396

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/21/2017, 11:46:20 AM · Difficulty 10.9026 · 4,671,630 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

05db9596bf443f3f4e8dc4e6248d3aa07aa25bc70e923b43ce4b5fc98cc4f4b5

View on Chainz ↗

Height

#2,170,396

Difficulty

10.902632

Transactions

Size

3.39 KB

Version

Bits

0ae712e9

Nonce

400,123,303

Timestamp

6/21/2017, 11:46:20 AM

Confirmations

4,671,630

Mined by

⛏️ P2SHAdZY2tmmvcCCGuevA98XK1HMX9yLiHwgPd

Merkle Root

0b04ab790ea20472b588eeb2b23fbbc77109f001ff5aec32c02d59768ea89634

Transactions (5)

Coinbase6c7dfd77079b57…4bfe2d95880d74

1 in → 1 out8.4600 XPM110 B

AdZY2tmm…yLiHwgPd

ec81cf309adb7f…51cee62ede0538

1 in → 2 out331870.4621 XPM227 B

AdpQwam3…cGk6VCiS AGxTvNB2…rSqrZ51D

db78fa43edb18f…8cad86998c175a

1 in → 2 out50203.5116 XPM226 B

AU87Hary…c9fUizfz AUVd2QD4…shtdrMnc

2fe80dab2f3c9b…3ef94317929975

10 in → 2 out115.0342 XPM1.52 KB

ARbNHS4z…vaKfFuuj AJT5ZDj4…DtnSSE5g

d9d3103cb0e162…0af57fd770fe48

8 in → 2 out38.5349 XPM1.23 KB

AKjHZoCN…1PWsDPDp AWxPhmaM…68LBBuJQ

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.

5.059 × 10⁹⁵(96-digit number)

50593087962586464157…79083104284548157439

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

5.059 × 10⁹⁵(96-digit number)

50593087962586464157…79083104284548157439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.059 × 10⁹⁵(96-digit number)

50593087962586464157…79083104284548157441

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

1.011 × 10⁹⁶(97-digit number)

10118617592517292831…58166208569096314879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.011 × 10⁹⁶(97-digit number)

10118617592517292831…58166208569096314881

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

2.023 × 10⁹⁶(97-digit number)

20237235185034585662…16332417138192629759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.023 × 10⁹⁶(97-digit number)

20237235185034585662…16332417138192629761

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

4.047 × 10⁹⁶(97-digit number)

40474470370069171325…32664834276385259519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.047 × 10⁹⁶(97-digit number)

40474470370069171325…32664834276385259521

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

8.094 × 10⁹⁶(97-digit number)

80948940740138342651…65329668552770519039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.094 × 10⁹⁶(97-digit number)

80948940740138342651…65329668552770519041

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 #2,170,396

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