Block #284,382

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 2:46:59 AM · Difficulty 9.9826 · 6,523,069 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

40c6a09d19d90f23f29f907fb5e2cc34ed15c7821ce01e9daeb326a039214d51

View on Chainz ↗

Height

#284,382

Difficulty

9.982622

Transactions

Size

2.96 KB

Version

Bits

09fb8d1b

Nonce

28,927

Timestamp

11/30/2013, 2:46:59 AM

Confirmations

6,523,069

Mined by

⛏️ P2SHAYaTpnoDjg4iRHnzSs6AaFf5TqEJq25nUy

Merkle Root

0aec1abaa7a7589ca6117bab0e4b3b6258f232f3c48fd8f171d763980863b1a1

Transactions (4)

Coinbase7a051f48525a40…a02c576e130a58

1 in → 2 out10.0600 XPM140 B

AYaTpnoD…EJq25nUy ASNt3cJa…L5zCqAYM

9dcf3caf807aad…1ab061a3c6e134

3 in → 1 out498.9700 XPM487 B

ATw57D22…TCbrFELg

8b2230a3ac5a6d…4526548e43fe69

3 in → 2 out48.0276 XPM521 B

AcEyZEmj…VkjtaGB9 ATdNw8in…r3e8T4CR

1844359cd2854e…2926d2318db3e3

10 in → 14 out51.2361 XPM1.75 KB

APeoSKP6…QVsJJKDK AeEfsV8M…YKaWhQ3f AKteWvxU…XQqfExXj AeKNrjNj…1NEq95Ta AYpANtX5…cpBRh2BL

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.

1.276 × 10⁹⁷(98-digit number)

12760935593738603735…66655806815677311999

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

1.276 × 10⁹⁷(98-digit number)

12760935593738603735…66655806815677311999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.276 × 10⁹⁷(98-digit number)

12760935593738603735…66655806815677312001

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

2.552 × 10⁹⁷(98-digit number)

25521871187477207470…33311613631354623999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.552 × 10⁹⁷(98-digit number)

25521871187477207470…33311613631354624001

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

5.104 × 10⁹⁷(98-digit number)

51043742374954414941…66623227262709247999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.104 × 10⁹⁷(98-digit number)

51043742374954414941…66623227262709248001

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

1.020 × 10⁹⁸(99-digit number)

10208748474990882988…33246454525418495999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.020 × 10⁹⁸(99-digit number)

10208748474990882988…33246454525418496001

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

2.041 × 10⁹⁸(99-digit number)

20417496949981765976…66492909050836991999

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 #284,382

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