Block #2,634,035

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2018, 5:46:13 PM · Difficulty 11.2193 · 4,205,747 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e1175a7c84521e9ed65e1a93c8d7941637bcffef53fa3ae6f93149e3a2fdaf79

View on Chainz ↗

Height

#2,634,035

Difficulty

11.219322

Transactions

Size

542 B

Version

Bits

0b38257e

Nonce

1,328,466,485

Timestamp

4/28/2018, 5:46:13 PM

Confirmations

4,205,747

Mined by

⛏️ P2SHASLuTrXKvpvLwRuDqt2oSETtW1KUnW1jjj

Merkle Root

6d85417b32aec1db84a43568c7d2c683956098082f26513e34bb903699e2bfbd

Transactions (2)

Coinbaseb60eb8a23394db…4a892d024613c2

1 in → 1 out7.9400 XPM110 B

ASLuTrXK…KUnW1jjj

4c2f29c9fb1878…5e01b8a2a0857a

2 in → 2 out11.6181 XPM342 B

ANd5Ah92…CcbLFra1 ALdjb6um…WuaWJUSs

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.

8.947 × 10⁹⁴(95-digit number)

89476168848155623273…42528664663087715839

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

8.947 × 10⁹⁴(95-digit number)

89476168848155623273…42528664663087715839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.947 × 10⁹⁴(95-digit number)

89476168848155623273…42528664663087715841

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

1.789 × 10⁹⁵(96-digit number)

17895233769631124654…85057329326175431679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.789 × 10⁹⁵(96-digit number)

17895233769631124654…85057329326175431681

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

3.579 × 10⁹⁵(96-digit number)

35790467539262249309…70114658652350863359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.579 × 10⁹⁵(96-digit number)

35790467539262249309…70114658652350863361

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

7.158 × 10⁹⁵(96-digit number)

71580935078524498618…40229317304701726719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.158 × 10⁹⁵(96-digit number)

71580935078524498618…40229317304701726721

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

1.431 × 10⁹⁶(97-digit number)

14316187015704899723…80458634609403453439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.431 × 10⁹⁶(97-digit number)

14316187015704899723…80458634609403453441

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

2.863 × 10⁹⁶(97-digit number)

28632374031409799447…60917269218806906879

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 #2,634,035

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