Block #2,128,152

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/22/2017, 1:26:44 PM · Difficulty 10.9167 · 4,703,085 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

394162637d5663eac1f5a2bc532d086aa6e5a6bfd553b35cd9685334fd5d7d92

View on Chainz ↗

Height

#2,128,152

Difficulty

10.916729

Transactions

Size

1019 B

Version

Bits

0aeaaec3

Nonce

208,344,051

Timestamp

5/22/2017, 1:26:44 PM

Confirmations

4,703,085

Mined by

⛏️ P2SHAPpW1XxqbBp3iEsmEGWLQNzUVMrf9KabNn

Merkle Root

44ee054c8d81d9c9bba4f1f8c6c255792e063825879ee726e3edaab575b1786d

Transactions (2)

Coinbase2df20e961e94dc…69eb79d62b33fb

1 in → 1 out8.3900 XPM110 B

APpW1Xxq…rf9KabNn

cf4386ca28e50d…89ac231ec53b96

5 in → 2 out303.7567 XPM817 B

AcgW9G4q…GvZmj2F5 ATwLVwTG…iuyYX15g

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.

5.557 × 10⁹⁸(99-digit number)

55572739205500619529…27041746097118822399

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

5.557 × 10⁹⁸(99-digit number)

55572739205500619529…27041746097118822399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.557 × 10⁹⁸(99-digit number)

55572739205500619529…27041746097118822401

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

1.111 × 10⁹⁹(100-digit number)

11114547841100123905…54083492194237644799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.111 × 10⁹⁹(100-digit number)

11114547841100123905…54083492194237644801

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

2.222 × 10⁹⁹(100-digit number)

22229095682200247811…08166984388475289599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.222 × 10⁹⁹(100-digit number)

22229095682200247811…08166984388475289601

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

4.445 × 10⁹⁹(100-digit number)

44458191364400495623…16333968776950579199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.445 × 10⁹⁹(100-digit number)

44458191364400495623…16333968776950579201

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

8.891 × 10⁹⁹(100-digit number)

88916382728800991247…32667937553901158399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.891 × 10⁹⁹(100-digit number)

88916382728800991247…32667937553901158401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.778 × 10¹⁰⁰(101-digit number)

17783276545760198249…65335875107802316799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,128,152

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