Block #2,633,442

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2018, 10:48:32 AM · Difficulty 11.1918 · 4,203,544 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

82e4a4192a839f21dc8a6bd2e4148e7822a533ad8870e03d4b7d20d87c8bc5db

View on Chainz ↗

Height

#2,633,442

Difficulty

11.191789

Transactions

Size

424 B

Version

Bits

0b31190e

Nonce

943,817,667

Timestamp

4/28/2018, 10:48:32 AM

Confirmations

4,203,544

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

655a9b558c7c9e4749fe41754e3fbf70fc46e75c9a608528f1c9cfdd9033d2e3

Transactions (2)

Coinbaseec80bedad7a6c2…04db4faedeb120

1 in → 1 out7.9800 XPM109 B

Adqah8zh…1WwoHJ9t

3b38144ae6fbfc…e0e5cfe21bc863

1 in → 2 out5.8354 XPM226 B

AHWbzLRF…fvcBqSkr AKCSvoxS…pqXFEBhu

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.

2.501 × 10⁹³(94-digit number)

25015674418660660245…75554193760382640359

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

2.501 × 10⁹³(94-digit number)

25015674418660660245…75554193760382640359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.501 × 10⁹³(94-digit number)

25015674418660660245…75554193760382640361

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

5.003 × 10⁹³(94-digit number)

50031348837321320491…51108387520765280719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.003 × 10⁹³(94-digit number)

50031348837321320491…51108387520765280721

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

1.000 × 10⁹⁴(95-digit number)

10006269767464264098…02216775041530561439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.000 × 10⁹⁴(95-digit number)

10006269767464264098…02216775041530561441

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

2.001 × 10⁹⁴(95-digit number)

20012539534928528196…04433550083061122879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.001 × 10⁹⁴(95-digit number)

20012539534928528196…04433550083061122881

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

4.002 × 10⁹⁴(95-digit number)

40025079069857056393…08867100166122245759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.002 × 10⁹⁴(95-digit number)

40025079069857056393…08867100166122245761

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

8.005 × 10⁹⁴(95-digit number)

80050158139714112786…17734200332244491519

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 #2,633,442

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