Block #1,600,648

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/26/2016, 10:06:53 AM · Difficulty 10.5988 · 5,213,389 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

abaa0b01fa821a21c00d760dfe92d0fea240d1e81cde57d12e0b71e4b1c19747

View on Chainz ↗

Height

#1,600,648

Difficulty

10.598768

Transactions

Size

1.05 KB

Version

Bits

0a9948e4

Nonce

761,939,686

Timestamp

5/26/2016, 10:06:53 AM

Confirmations

5,213,389

Mined by

⛏️ P2SHANK36VGV8VvBVbWPQwcucff7ALbSLRKPFb

Merkle Root

aee24931f82436350f60374d9d4a5cd99abc58ebf1273886f46230b7828f075d

Transactions (2)

Coinbase484835c2e4fb9a…5def211d9aabad

1 in → 1 out8.9000 XPM110 B

ANK36VGV…bSLRKPFb

0760c50a5c463b…7b1aa77a750e44

1 in → 21 out297.5183 XPM873 B

AaGjuneM…kUhKSege ARSGwfvq…RdvnptaP ASVuvy7C…KvJZavfQ AKiEj23g…tUKfd1XY AYVQ3hHz…Ce6whb4U

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.

6.571 × 10⁹⁴(95-digit number)

65711486059513636007…71476554238797618559

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

6.571 × 10⁹⁴(95-digit number)

65711486059513636007…71476554238797618559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.571 × 10⁹⁴(95-digit number)

65711486059513636007…71476554238797618561

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

1.314 × 10⁹⁵(96-digit number)

13142297211902727201…42953108477595237119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.314 × 10⁹⁵(96-digit number)

13142297211902727201…42953108477595237121

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

2.628 × 10⁹⁵(96-digit number)

26284594423805454402…85906216955190474239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.628 × 10⁹⁵(96-digit number)

26284594423805454402…85906216955190474241

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

5.256 × 10⁹⁵(96-digit number)

52569188847610908805…71812433910380948479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.256 × 10⁹⁵(96-digit number)

52569188847610908805…71812433910380948481

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

1.051 × 10⁹⁶(97-digit number)

10513837769522181761…43624867820761896959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.051 × 10⁹⁶(97-digit number)

10513837769522181761…43624867820761896961

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 #1,600,648

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