Block #244,591

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/4/2013, 11:18:15 PM · Difficulty 9.9630 · 6,569,709 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8fdf0a23da52c1f66713b9c0a2ef89e96a3c3f12b624df8c9cbae0a12dd58c8e

View on Chainz ↗

Height

#244,591

Difficulty

9.962998

Transactions

Size

15.88 KB

Version

Bits

09f6870f

Nonce

957

Timestamp

11/4/2013, 11:18:15 PM

Confirmations

6,569,709

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

2c3fdf146c11195c55c56a04aa5c4686f8fd17f10ae923a0c1e345106d4eb47f

Transactions (2)

Coinbased9ecbd3037d267…7faa26d3887f45

1 in → 2 out10.2300 XPM136 B

AZDUEbdS…RYKMRZET ALfEGCwh…VawujfMm

2c523db13d6f56…15350d9a485566

108 in → 1 out24.8082 XPM15.66 KB

ASePrqts…mAVvmZb9

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.

1.777 × 10⁹⁹(100-digit number)

17773820595110094844…22415547044257942219

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

1.777 × 10⁹⁹(100-digit number)

17773820595110094844…22415547044257942219

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.777 × 10⁹⁹(100-digit number)

17773820595110094844…22415547044257942221

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

3.554 × 10⁹⁹(100-digit number)

35547641190220189689…44831094088515884439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.554 × 10⁹⁹(100-digit number)

35547641190220189689…44831094088515884441

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

7.109 × 10⁹⁹(100-digit number)

71095282380440379379…89662188177031768879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.109 × 10⁹⁹(100-digit number)

71095282380440379379…89662188177031768881

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

1.421 × 10¹⁰⁰(101-digit number)

14219056476088075875…79324376354063537759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.421 × 10¹⁰⁰(101-digit number)

14219056476088075875…79324376354063537761

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

2.843 × 10¹⁰⁰(101-digit number)

28438112952176151751…58648752708127075519

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

Block #244,591

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