Block #1,628,887

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/15/2016, 12:17:16 AM · Difficulty 10.6020 · 5,211,572 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

265a54372b41f1729a857c762cf8ae414a8f570c708ec8a16bd0f0f54e0051e1

View on Chainz ↗

Height

#1,628,887

Difficulty

10.602004

Transactions

Size

390 B

Version

Bits

0a9a1cee

Nonce

96,551,722

Timestamp

6/15/2016, 12:17:16 AM

Confirmations

5,211,572

Mined by

⛏️ P2SHAdCeNvJZqjei94wG4SKvFZGibkRbZaDiLb

Merkle Root

89a632bf49a1091dce2bbc6755f0f75655ae0de149c8f8a1034a9e6a0da497d1

Transactions (2)

Coinbase2c6921c40f5217…fc3c9e63032f1d

1 in → 1 out8.8900 XPM109 B

AdCeNvJZ…RbZaDiLb

9e380417822889…25243953fa0751

1 in → 1 out999.9900 XPM191 B

AcDhjHA9…ebukETHz

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.

1.452 × 10⁹⁵(96-digit number)

14520920803933250569…13123882620783549439

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

1.452 × 10⁹⁵(96-digit number)

14520920803933250569…13123882620783549439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.452 × 10⁹⁵(96-digit number)

14520920803933250569…13123882620783549441

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

2.904 × 10⁹⁵(96-digit number)

29041841607866501138…26247765241567098879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.904 × 10⁹⁵(96-digit number)

29041841607866501138…26247765241567098881

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

5.808 × 10⁹⁵(96-digit number)

58083683215733002277…52495530483134197759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.808 × 10⁹⁵(96-digit number)

58083683215733002277…52495530483134197761

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

1.161 × 10⁹⁶(97-digit number)

11616736643146600455…04991060966268395519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.161 × 10⁹⁶(97-digit number)

11616736643146600455…04991060966268395521

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

2.323 × 10⁹⁶(97-digit number)

23233473286293200911…09982121932536791039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.323 × 10⁹⁶(97-digit number)

23233473286293200911…09982121932536791041

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 #1,628,887

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