Block #244,911

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/5/2013, 4:04:16 AM · Difficulty 9.9633 · 6,564,889 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f89b2cbd455a62ffc783134a70ef0ada862e11f8f293f24ad457ccf9d964bba5

View on Chainz ↗

Height

#244,911

Difficulty

9.963264

Transactions

Size

1.91 KB

Version

Bits

09f69876

Nonce

2,730

Timestamp

11/5/2013, 4:04:16 AM

Confirmations

6,564,889

Mined by

⛏️ Rxn'1AcQu7YS3bmebYvsM5YRYAHL34GuUFynwty

Merkle Root

98dcdee5040227960c0723148144daa169f6c10557af42874c023effae719339

Transactions (1)

Coinbase98dcdee5040227…023effae719339

1 in → 53 out10.0400 XPM1.82 KB

AcQu7YS3…uUFynwty ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC AZWiC56x…NwextJca AMbCuLHZ…WSoStwkc

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.

7.082 × 10⁹⁶(97-digit number)

70820130062120311707…80122514472353596799

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

7.082 × 10⁹⁶(97-digit number)

70820130062120311707…80122514472353596799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.082 × 10⁹⁶(97-digit number)

70820130062120311707…80122514472353596801

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

1.416 × 10⁹⁷(98-digit number)

14164026012424062341…60245028944707193599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.416 × 10⁹⁷(98-digit number)

14164026012424062341…60245028944707193601

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

2.832 × 10⁹⁷(98-digit number)

28328052024848124682…20490057889414387199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.832 × 10⁹⁷(98-digit number)

28328052024848124682…20490057889414387201

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

5.665 × 10⁹⁷(98-digit number)

56656104049696249365…40980115778828774399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.665 × 10⁹⁷(98-digit number)

56656104049696249365…40980115778828774401

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

1.133 × 10⁹⁸(99-digit number)

11331220809939249873…81960231557657548799

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 #244,911

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