Block #299,869

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/8/2013, 6:09:21 AM · Difficulty 9.9922 · 6,512,869 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2c5db8667ffe566c49372792733b445d442b92d78474701ea47b5f6f3a99e143

View on Chainz ↗

Height

#299,869

Difficulty

9.992164

Transactions

Size

647 B

Version

Bits

09fdfe7c

Nonce

12,710

Timestamp

12/8/2013, 6:09:21 AM

Confirmations

6,512,869

Mined by

⛏️ P2SHAb11MejzqGsVp8Wn9HtBJLqWnGjo2QsXa5

Merkle Root

9271360c7575cf6d43548b852cde2258a064a6ba59fe2e130546a619faddcae4

Transactions (3)

Coinbase5294f7e4d7a0a0…788c4f37dade10

1 in → 1 out10.0200 XPM109 B

Ab11Mejz…jo2QsXa5

176d87f3c58b77…0e50bed0b59d7b

1 in → 2 out34.7865 XPM225 B

AL9dbFE7…7twjL1Dp AJdvJmjS…GFTusQmv

65f7729edcb296…bb752c856217d9

1 in → 2 out300.0243 XPM225 B

AUXLXspt…iWERtYuZ AU73Y7hQ…wjgmDCfv

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.

1.003 × 10⁹¹(92-digit number)

10033848396539948806…93426633939421630259

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

1.003 × 10⁹¹(92-digit number)

10033848396539948806…93426633939421630259

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.003 × 10⁹¹(92-digit number)

10033848396539948806…93426633939421630261

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

2.006 × 10⁹¹(92-digit number)

20067696793079897613…86853267878843260519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.006 × 10⁹¹(92-digit number)

20067696793079897613…86853267878843260521

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

4.013 × 10⁹¹(92-digit number)

40135393586159795227…73706535757686521039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.013 × 10⁹¹(92-digit number)

40135393586159795227…73706535757686521041

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

8.027 × 10⁹¹(92-digit number)

80270787172319590454…47413071515373042079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.027 × 10⁹¹(92-digit number)

80270787172319590454…47413071515373042081

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

1.605 × 10⁹²(93-digit number)

16054157434463918090…94826143030746084159

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 #299,869

Cookie Preferences