Block #2,632,835

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2018, 2:11:39 AM · Difficulty 11.1776 · 4,206,112 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

28e655aa733c6ed24b4f9bfadf0e34b297a81b81facdb381fe856c990fcf6cf7

View on Chainz ↗

Height

#2,632,835

Difficulty

11.177554

Transactions

Size

1.37 KB

Version

Bits

0b2d7433

Nonce

676,008,008

Timestamp

4/28/2018, 2:11:39 AM

Confirmations

4,206,112

Mined by

⛏️ P2SHAY22rPk4BCsd5KnyZTsNAxFWPXR8SC7TuY

Merkle Root

268112a120fa06a3dc503365b3f2049368e1f3e690127faba64b58fa3b193e90

Transactions (5)

Coinbase39fe69b7d5e275…a170b8f7cbdb19

1 in → 1 out8.0300 XPM110 B

AY22rPk4…R8SC7TuY

077ae11d306a5f…5311d19db56ece

3 in → 2 out5040.3662 XPM523 B

AJVKK2SH…WyGthNL3 AWjkKTjp…rn4kctd5

b50376f45c45be…c57e92c59a0dbc

1 in → 2 out1292.3120 XPM225 B

AMqBmWko…VYp42XyH AevTGMvf…9qeUqAZU

fb0c5bcb956b84…2e51051b237f11

1 in → 2 out126043.0291 XPM227 B

AFnNwCQ9…iywgHYkL APCX6jdi…MToeULJF

b4bc0b92323c62…aabd940fe5e628

1 in → 2 out124052.0241 XPM226 B

ASBDxkQU…fzeL3BRP AV7eBPPS…Cg2JWp5U

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.

1.134 × 10⁹⁹(100-digit number)

11342192580037119571…21650505378737848319

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

1.134 × 10⁹⁹(100-digit number)

11342192580037119571…21650505378737848319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.134 × 10⁹⁹(100-digit number)

11342192580037119571…21650505378737848321

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

2.268 × 10⁹⁹(100-digit number)

22684385160074239142…43301010757475696639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.268 × 10⁹⁹(100-digit number)

22684385160074239142…43301010757475696641

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

4.536 × 10⁹⁹(100-digit number)

45368770320148478284…86602021514951393279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.536 × 10⁹⁹(100-digit number)

45368770320148478284…86602021514951393281

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

9.073 × 10⁹⁹(100-digit number)

90737540640296956568…73204043029902786559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.073 × 10⁹⁹(100-digit number)

90737540640296956568…73204043029902786561

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

1.814 × 10¹⁰⁰(101-digit number)

18147508128059391313…46408086059805573119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.814 × 10¹⁰⁰(101-digit number)

18147508128059391313…46408086059805573121

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

3.629 × 10¹⁰⁰(101-digit number)

36295016256118782627…92816172119611146239

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 #2,632,835

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