Block #3,528,179

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/24/2020, 4:01:06 AM · Difficulty 10.9361 · 3,313,918 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e8426739280adbe1c175d7ed87001dd980e0c6a8a027f592eb26141df0b2c7e5

View on Chainz ↗

Height

#3,528,179

Difficulty

10.936101

Transactions

Size

8.52 KB

Version

Bits

0aefa458

Nonce

666,544,536

Timestamp

1/24/2020, 4:01:06 AM

Confirmations

3,313,918

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

168ed5bfa0a0915f0a7b0eb974c373738ea9fdf258ed4b51c1c94fa3c0720ef5

Transactions (3)

Coinbased5ede4bf6c21c1…a2902d9f06d229

1 in → 1 out8.4400 XPM110 B

ASiq2qtK…VMhmk7yL

b2b2a4a528c085…3d484b43a123c3

60 in → 2 out500.3300 XPM6.76 KB

ASiq2qtK…VMhmk7yL Ab5fFXVt…EC9k8a2d

dcad7972250bbf…3752818248b501

13 in → 2 out100.1618 XPM1.56 KB

ASiq2qtK…VMhmk7yL AccU5sZ8…GCwu6tgM

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.

3.445 × 10⁹⁶(97-digit number)

34457271262492444892…82342971817077052799

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

3.445 × 10⁹⁶(97-digit number)

34457271262492444892…82342971817077052799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.445 × 10⁹⁶(97-digit number)

34457271262492444892…82342971817077052801

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

6.891 × 10⁹⁶(97-digit number)

68914542524984889784…64685943634154105599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.891 × 10⁹⁶(97-digit number)

68914542524984889784…64685943634154105601

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

1.378 × 10⁹⁷(98-digit number)

13782908504996977956…29371887268308211199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.378 × 10⁹⁷(98-digit number)

13782908504996977956…29371887268308211201

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

2.756 × 10⁹⁷(98-digit number)

27565817009993955913…58743774536616422399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.756 × 10⁹⁷(98-digit number)

27565817009993955913…58743774536616422401

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

5.513 × 10⁹⁷(98-digit number)

55131634019987911827…17487549073232844799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.513 × 10⁹⁷(98-digit number)

55131634019987911827…17487549073232844801

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 #3,528,179

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