Block #279,699

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 10:39:18 AM · Difficulty 9.9725 · 6,510,441 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f01f2642ee489c6e264d1e4e04b3e895680f8d3ec86176326a4c6419d3fa76fa

View on Chainz ↗

Height

#279,699

Difficulty

9.972518

Transactions

Size

1.44 KB

Version

Bits

09f8f6ed

Nonce

18,266

Timestamp

11/28/2013, 10:39:18 AM

Confirmations

6,510,441

Merkle Root

e4748eb891deb6b743a95e33c938d8f6316038fc3eedb896d31b2b7f39751bb8

Transactions (4)

Coinbaseb7bf17fa186442…ceb88a0466b931

1 in → 1 out10.1100 XPM110 B

AeKNrjNj…1NEq95Ta

faaa6fccffa775…5d1b93f5398834

4 in → 2 out211.1760 XPM671 B

AHQeZ6ok…xCzrGt7h AeLKKFyT…zAvZruxa

76f04e9a71ef20…e7b78552baf47b

1 in → 2 out3.0135 XPM226 B

ASHAmHBt…4ZKbdSkJ AePRWBYd…jQhu5Sx3

caf8b6c9e9b3b3…b17bb81a149c46

2 in → 2 out1.6455 XPM375 B

AcCEfvsX…48fyTE4c AcgoumAq…euzFj4Re

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.

8.301 × 10⁹⁴(95-digit number)

83017702908466673668…19980939056384427519

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

8.301 × 10⁹⁴(95-digit number)

83017702908466673668…19980939056384427519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.301 × 10⁹⁴(95-digit number)

83017702908466673668…19980939056384427521

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

1.660 × 10⁹⁵(96-digit number)

16603540581693334733…39961878112768855039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.660 × 10⁹⁵(96-digit number)

16603540581693334733…39961878112768855041

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

3.320 × 10⁹⁵(96-digit number)

33207081163386669467…79923756225537710079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.320 × 10⁹⁵(96-digit number)

33207081163386669467…79923756225537710081

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

6.641 × 10⁹⁵(96-digit number)

66414162326773338935…59847512451075420159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.641 × 10⁹⁵(96-digit number)

66414162326773338935…59847512451075420161

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

1.328 × 10⁹⁶(97-digit number)

13282832465354667787…19695024902150840319

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