Block #279,469

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 8:50:29 AM · Difficulty 9.9718 · 6,545,999 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4c067c57e97a5a39428289bdbf12b823a87d3841cbed658bd89a61f15ad13d0e

View on Chainz ↗

Height

#279,469

Difficulty

9.971836

Transactions

Size

1.08 KB

Version

Bits

09f8ca42

Nonce

96,523

Timestamp

11/28/2013, 8:50:29 AM

Confirmations

6,545,999

Mined by

⛏️ CaRAScAzqGcxPcDWPrubeWQJ2B4ezBZ6tV1vJ

Merkle Root

3d1f52743b7714c0668baa1865a1dbc08ef0c5cf6b73c4d3d65087000cba7a7f

Transactions (1)

Coinbase3d1f52743b7714…5087000cba7a7f

1 in → 28 out10.0200 XPM1015 B

AScAzqGc…BZ6tV1vJ AZ2pPuKg…95SN2Yr7 AHV2J3tP…7ZwLJbDZ AMbCuLHZ…WSoStwkc APFsQ3Fo…xoFKrF12

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.

1.090 × 10¹⁰⁰(101-digit number)

10902717519665468023…87972877936738734079

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

1.090 × 10¹⁰⁰(101-digit number)

10902717519665468023…87972877936738734079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.090 × 10¹⁰⁰(101-digit number)

10902717519665468023…87972877936738734081

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

2.180 × 10¹⁰⁰(101-digit number)

21805435039330936047…75945755873477468159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.180 × 10¹⁰⁰(101-digit number)

21805435039330936047…75945755873477468161

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

4.361 × 10¹⁰⁰(101-digit number)

43610870078661872095…51891511746954936319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.361 × 10¹⁰⁰(101-digit number)

43610870078661872095…51891511746954936321

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

8.722 × 10¹⁰⁰(101-digit number)

87221740157323744190…03783023493909872639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.722 × 10¹⁰⁰(101-digit number)

87221740157323744190…03783023493909872641

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

1.744 × 10¹⁰¹(102-digit number)

17444348031464748838…07566046987819745279

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 #279,469

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