Block #234,652

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/30/2013, 11:18:10 AM · Difficulty 9.9443 · 6,563,933 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7e921e0c89972bc01dd66d41bc60ba036980deb9c70597cacc375c4f63ba60b8

View on Chainz ↗

Height

#234,652

Difficulty

9.944284

Transactions

Size

802 B

Version

Bits

09f1bc9c

Nonce

40,522

Timestamp

10/30/2013, 11:18:10 AM

Confirmations

6,563,933

Mined by

⛏️ P2SHAZ9gwDSQ9eWoQY9W5dUGn7b9Zwha77qwDk

Merkle Root

5dff32defdab525146ee306f0b537d56903d368772a24a03bb9b826a8e6d89cf

Transactions (3)

Coinbase69592bc795b7f7…87f08bf2ef8a48

1 in → 1 out10.1200 XPM109 B

AZ9gwDSQ…ha77qwDk

9c768a21986a23…590ee19da09d52

1 in → 2 out10.0900 XPM227 B

AFxNiSFx…XK4camWq ALL6BtTJ…cp6j3qpk

f5781857178360…65f1c7c1e889c1

2 in → 2 out15.7742 XPM373 B

ASuoUi24…FwBoFbxd AcY78Kzk…F5C49QGk

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.

8.908 × 10¹⁰¹(102-digit number)

89089981276490418696…93404799958568849919

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

8.908 × 10¹⁰¹(102-digit number)

89089981276490418696…93404799958568849919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.908 × 10¹⁰¹(102-digit number)

89089981276490418696…93404799958568849921

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

1.781 × 10¹⁰²(103-digit number)

17817996255298083739…86809599917137699839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.781 × 10¹⁰²(103-digit number)

17817996255298083739…86809599917137699841

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

3.563 × 10¹⁰²(103-digit number)

35635992510596167478…73619199834275399679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.563 × 10¹⁰²(103-digit number)

35635992510596167478…73619199834275399681

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

7.127 × 10¹⁰²(103-digit number)

71271985021192334957…47238399668550799359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.127 × 10¹⁰²(103-digit number)

71271985021192334957…47238399668550799361

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

1.425 × 10¹⁰³(104-digit number)

14254397004238466991…94476799337101598719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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