Block #2,643,267

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/2/2018, 1:14:58 AM · Difficulty 11.6783 · 4,187,457 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

99aa2e2cc84ad968e8c6a13414092e08ff99b1603e70c1524047a7d4173a15d1

View on Chainz ↗

Height

#2,643,267

Difficulty

11.678252

Transactions

Size

800 B

Version

Bits

0bada1f2

Nonce

221,931,442

Timestamp

5/2/2018, 1:14:58 AM

Confirmations

4,187,457

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

b1b284e8ccad61ee6fc0bf509ff0c1734f501da56918fda62378cae15dd1536f

Transactions (3)

Coinbase5e53f6a6fed1f2…28a5c5a24eef93

1 in → 1 out7.3400 XPM110 B

Adqah8zh…1WwoHJ9t

77ef66935f47bc…453d322696b0f0

1 in → 2 out12.6716 XPM226 B

APi8C85f…Lg5MDiei ALJBanQH…h8uqYjKT

d409e6c0210b13…ae2a64c18c0dc8

2 in → 2 out21.8884 XPM374 B

ATJ2NbJC…RSoovzGw AFs1CvBJ…E5x1acTU

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.

1.179 × 10⁹⁵(96-digit number)

11795550329581445334…46321341791570895359

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

1.179 × 10⁹⁵(96-digit number)

11795550329581445334…46321341791570895359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.179 × 10⁹⁵(96-digit number)

11795550329581445334…46321341791570895361

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

2.359 × 10⁹⁵(96-digit number)

23591100659162890668…92642683583141790719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.359 × 10⁹⁵(96-digit number)

23591100659162890668…92642683583141790721

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

4.718 × 10⁹⁵(96-digit number)

47182201318325781336…85285367166283581439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.718 × 10⁹⁵(96-digit number)

47182201318325781336…85285367166283581441

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

9.436 × 10⁹⁵(96-digit number)

94364402636651562672…70570734332567162879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.436 × 10⁹⁵(96-digit number)

94364402636651562672…70570734332567162881

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

1.887 × 10⁹⁶(97-digit number)

18872880527330312534…41141468665134325759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.887 × 10⁹⁶(97-digit number)

18872880527330312534…41141468665134325761

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

3.774 × 10⁹⁶(97-digit number)

37745761054660625068…82282937330268651519

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 #2,643,267

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