Block #3,655,058

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/23/2020, 7:37:14 AM · Difficulty 10.8907 · 3,190,273 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

27963f6ebd5ac8d3a874b372aab4e023977413db33ebb5836b1e5936ce2977bc

View on Chainz ↗

Height

#3,655,058

Difficulty

10.890721

Transactions

Size

574 B

Version

Bits

0ae40653

Nonce

2,070,514,638

Timestamp

4/23/2020, 7:37:14 AM

Confirmations

3,190,273

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

2edf078a57417976a1de9a68148ca46af5ca84eeefbe4258f899d0a4b79ce209

Transactions (2)

Coinbasea86f663488abf8…a37a185baf4914

1 in → 1 out8.5200 XPM109 B

ASiq2qtK…VMhmk7yL

1908f0757e77d6…52592ce4942d82

2 in → 2 out3542.6504 XPM374 B

ARAgbnSi…dPcPH5uM AFnhfyw9…AyM5Lz6f

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.

1.616 × 10⁹⁷(98-digit number)

16169954545182271697…74251760506832486399

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

1.616 × 10⁹⁷(98-digit number)

16169954545182271697…74251760506832486399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.616 × 10⁹⁷(98-digit number)

16169954545182271697…74251760506832486401

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

3.233 × 10⁹⁷(98-digit number)

32339909090364543395…48503521013664972799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.233 × 10⁹⁷(98-digit number)

32339909090364543395…48503521013664972801

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

6.467 × 10⁹⁷(98-digit number)

64679818180729086791…97007042027329945599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.467 × 10⁹⁷(98-digit number)

64679818180729086791…97007042027329945601

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

1.293 × 10⁹⁸(99-digit number)

12935963636145817358…94014084054659891199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.293 × 10⁹⁸(99-digit number)

12935963636145817358…94014084054659891201

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

2.587 × 10⁹⁸(99-digit number)

25871927272291634716…88028168109319782399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.587 × 10⁹⁸(99-digit number)

25871927272291634716…88028168109319782401

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 #3,655,058

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