Block #286,907

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/1/2013, 2:23:14 AM · Difficulty 9.9861 · 6,510,005 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7b31935c15fdff40b7f3bbc5d96d5cd41fbaf0efd7c93ae4228fbd952ba8569d

View on Chainz ↗

Height

#286,907

Difficulty

9.986120

Transactions

Size

836 B

Version

Bits

09fc7260

Nonce

34,218

Timestamp

12/1/2013, 2:23:14 AM

Confirmations

6,510,005

Mined by

⛏️ P2SHAYaTpnoDjg4iRHnzSs6AaFf5TqEJq25nUy

Merkle Root

16bd2ccfedb6262912677e1196f33c2a833c261047a62331bb78a42b8f39e9fc

Transactions (3)

Coinbase23a5756d84e43b…9c441436933475

1 in → 2 out10.0300 XPM141 B

AYaTpnoD…EJq25nUy ALfEGCwh…VawujfMm

7671714a3f40e9…f3a3f82b7cc827

2 in → 2 out1.4262 XPM375 B

AH96ok2E…BzcuEhPt AVWj3J2F…s8P6MeF8

ef0f34d017b953…130fac633c953d

1 in → 2 out1.5279 XPM226 B

AXUaFiig…VnF9BePY AJhPXGSS…SoByLABc

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.

3.001 × 10¹⁰³(104-digit number)

30019990990838951372…02216270433826462139

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

3.001 × 10¹⁰³(104-digit number)

30019990990838951372…02216270433826462139

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.001 × 10¹⁰³(104-digit number)

30019990990838951372…02216270433826462141

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

6.003 × 10¹⁰³(104-digit number)

60039981981677902745…04432540867652924279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.003 × 10¹⁰³(104-digit number)

60039981981677902745…04432540867652924281

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

1.200 × 10¹⁰⁴(105-digit number)

12007996396335580549…08865081735305848559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.200 × 10¹⁰⁴(105-digit number)

12007996396335580549…08865081735305848561

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

2.401 × 10¹⁰⁴(105-digit number)

24015992792671161098…17730163470611697119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.401 × 10¹⁰⁴(105-digit number)

24015992792671161098…17730163470611697121

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

4.803 × 10¹⁰⁴(105-digit number)

48031985585342322196…35460326941223394239

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