Block #286,852

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/1/2013, 1:43:40 AM · Difficulty 9.9861 · 6,523,137 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

60b3161a8dabbaf243c0385a578d5307b0ac082910a7f3c2269a49e4be9b4fb1

View on Chainz ↗

Height

#286,852

Difficulty

9.986076

Transactions

Size

722 B

Version

Bits

09fc6f81

Nonce

87,861

Timestamp

12/1/2013, 1:43:40 AM

Confirmations

6,523,137

Mined by

⛏️ P2SHAYaTpnoDjg4iRHnzSs6AaFf5TqEJq25nUy

Merkle Root

9d39bd5a59c67d8f4d8a3f0cbf8abae833ce86e882a33c2726c1a606f4d21b07

Transactions (2)

Coinbase1f70963fe6ab34…827e9a66c68bd5

1 in → 2 out10.0200 XPM142 B

AYaTpnoD…EJq25nUy AHsw4d6U…EnM8UXNZ

83092b4bc714fa…a1c09c96c7d8fc

3 in → 1 out66.6200 XPM486 B

AL6XnfzP…Acci5V6g

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.

1.169 × 10¹⁰⁴(105-digit number)

11691753244833198751…59758782636572316239

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

1.169 × 10¹⁰⁴(105-digit number)

11691753244833198751…59758782636572316239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.169 × 10¹⁰⁴(105-digit number)

11691753244833198751…59758782636572316241

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

2.338 × 10¹⁰⁴(105-digit number)

23383506489666397503…19517565273144632479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.338 × 10¹⁰⁴(105-digit number)

23383506489666397503…19517565273144632481

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

4.676 × 10¹⁰⁴(105-digit number)

46767012979332795007…39035130546289264959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.676 × 10¹⁰⁴(105-digit number)

46767012979332795007…39035130546289264961

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

9.353 × 10¹⁰⁴(105-digit number)

93534025958665590014…78070261092578529919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.353 × 10¹⁰⁴(105-digit number)

93534025958665590014…78070261092578529921

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

1.870 × 10¹⁰⁵(106-digit number)

18706805191733118002…56140522185157059839

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 #286,852

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