Block #2,632,927

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2018, 3:45:58 AM · Difficulty 11.1767 · 4,200,862 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2b59ccc3e04c4a5bb0f889f0194768c74ec8ba44c06d2baf43bb771d4e10e1a7

View on Chainz ↗

Height

#2,632,927

Difficulty

11.176717

Transactions

Size

609 B

Version

Bits

0b2d3d57

Nonce

146,269,518

Timestamp

4/28/2018, 3:45:58 AM

Confirmations

4,200,862

Mined by

⛏️ P2SHAZ6AfLLdHa2kyx3gtxgCWDus2GBRetzoJ8

Merkle Root

dddc9be26b2ddef682db688354953b955570c22d98aecdb5318b034fbe8e2d48

Transactions (2)

Coinbase69f33d3fb78431…95372ee9e88ea3

1 in → 1 out8.0000 XPM110 B

AZ6AfLLd…BRetzoJ8

b869266063fa5d…ee81d40d8fecae

2 in → 3 out219.2409 XPM408 B

AKg5sJMp…WaVCTNNt AUyF4p8T…G9CyDzgD ATQb3fYJ…W3EJsyW4

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.

9.550 × 10⁹⁵(96-digit number)

95508439928654556832…84315425654992369919

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

9.550 × 10⁹⁵(96-digit number)

95508439928654556832…84315425654992369919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.550 × 10⁹⁵(96-digit number)

95508439928654556832…84315425654992369921

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

1.910 × 10⁹⁶(97-digit number)

19101687985730911366…68630851309984739839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.910 × 10⁹⁶(97-digit number)

19101687985730911366…68630851309984739841

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

3.820 × 10⁹⁶(97-digit number)

38203375971461822732…37261702619969479679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.820 × 10⁹⁶(97-digit number)

38203375971461822732…37261702619969479681

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

7.640 × 10⁹⁶(97-digit number)

76406751942923645465…74523405239938959359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.640 × 10⁹⁶(97-digit number)

76406751942923645465…74523405239938959361

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

1.528 × 10⁹⁷(98-digit number)

15281350388584729093…49046810479877918719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.528 × 10⁹⁷(98-digit number)

15281350388584729093…49046810479877918721

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

3.056 × 10⁹⁷(98-digit number)

30562700777169458186…98093620959755837439

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 #2,632,927

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