Block #2,654,435

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 5/9/2018, 7:25:06 AM · Difficulty 11.7214 · 4,177,007 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2af237d5eda53027fcf8fcc45c62933544b2512ad4d85b191c61a560908c2b1d

View on Chainz ↗

Height

#2,654,435

Difficulty

11.721375

Transactions

Size

798 B

Version

Bits

0bb8ac02

Nonce

1,616,493,521

Timestamp

5/9/2018, 7:25:06 AM

Confirmations

4,177,007

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

2aab2ea573668248629cc0bf628f4a4537d5cbe063b5398945b47e24f966b790

Transactions (3)

Coinbase87da5a68788f26…38c8d00ca3fca2

1 in → 1 out7.2900 XPM110 B

Adqah8zh…1WwoHJ9t

289359d2f9dcd1…d426ca4fa7e7f0

1 in → 2 out107168.7600 XPM225 B

AVaQtWgv…EdQEqULx AVLZagFK…UrGC8xZL

478c8f1e90d7f9…e86ba9e7d6d8a1

2 in → 2 out0.1143 XPM373 B

AHoLDREh…3Yj9b4yY AN7b55gz…YroqkbjU

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.

9.424 × 10⁹³(94-digit number)

94248767205084680148…17527578498071868599

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

9.424 × 10⁹³(94-digit number)

94248767205084680148…17527578498071868599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.424 × 10⁹³(94-digit number)

94248767205084680148…17527578498071868601

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

1.884 × 10⁹⁴(95-digit number)

18849753441016936029…35055156996143737199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.884 × 10⁹⁴(95-digit number)

18849753441016936029…35055156996143737201

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

3.769 × 10⁹⁴(95-digit number)

37699506882033872059…70110313992287474399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.769 × 10⁹⁴(95-digit number)

37699506882033872059…70110313992287474401

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

7.539 × 10⁹⁴(95-digit number)

75399013764067744119…40220627984574948799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.539 × 10⁹⁴(95-digit number)

75399013764067744119…40220627984574948801

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

1.507 × 10⁹⁵(96-digit number)

15079802752813548823…80441255969149897599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.507 × 10⁹⁵(96-digit number)

15079802752813548823…80441255969149897601

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

3.015 × 10⁹⁵(96-digit number)

30159605505627097647…60882511938299795199

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

3.015 × 10⁹⁵(96-digit number)

30159605505627097647…60882511938299795201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #2,654,435

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