Block #299,784

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/8/2013, 4:58:59 AM · Difficulty 9.9921 · 6,492,807 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c40fdfda2f2ec9350fba6561ab062524022b98316170b6e71c4cf36fa6e68cf5

View on Chainz ↗

Height

#299,784

Difficulty

9.992139

Transactions

Size

1.11 KB

Version

Bits

09fdfcce

Nonce

120,357

Timestamp

12/8/2013, 4:58:59 AM

Confirmations

6,492,807

Merkle Root

09429bd9c53c95ce30ff820758aeedb53ee66ed02e3cdbaf350c5b22fd614d0e

Transactions (1)

Coinbase09429bd9c53c95…0c5b22fd614d0e

1 in → 29 out9.9800 XPM1.02 KB

Ad9pSzHt…cpJ3y2zz ASWX42VM…XypQABkY AHuJ9wYh…BGmgHrKZ AQwRN8bE…V8PsTcY9 APeshfYV…3PKcKMKH

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.

7.151 × 10⁹³(94-digit number)

71514204692571806695…04892460943835519999

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

7.151 × 10⁹³(94-digit number)

71514204692571806695…04892460943835519999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.151 × 10⁹³(94-digit number)

71514204692571806695…04892460943835520001

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

1.430 × 10⁹⁴(95-digit number)

14302840938514361339…09784921887671039999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.430 × 10⁹⁴(95-digit number)

14302840938514361339…09784921887671040001

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

2.860 × 10⁹⁴(95-digit number)

28605681877028722678…19569843775342079999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.860 × 10⁹⁴(95-digit number)

28605681877028722678…19569843775342080001

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

5.721 × 10⁹⁴(95-digit number)

57211363754057445356…39139687550684159999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.721 × 10⁹⁴(95-digit number)

57211363754057445356…39139687550684160001

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

1.144 × 10⁹⁵(96-digit number)

11442272750811489071…78279375101368319999

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