Block #285,724

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 2:48:40 PM · Difficulty 9.9847 · 6,506,789 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1b7ac2e075b839cbd634f725b36b26d7d8094f459ae97c7d4af22f9d1e61db28

View on Chainz ↗

Height

#285,724

Difficulty

9.984672

Transactions

Size

1.12 KB

Version

Bits

09fc1376

Nonce

2,246

Timestamp

11/30/2013, 2:48:40 PM

Confirmations

6,506,789

Merkle Root

111d35043472a5a248c0a240611957ace7b86bb5232c4ba6f9af805fe5654243

Transactions (1)

Coinbase111d35043472a5…af805fe5654243

1 in → 29 out10.0000 XPM1.02 KB

AVss9H5F…zXhyMijY AGqQ4WX6…HCR8xUMa AcC2zSod…rtWatH79 AWXYBWKP…qQAoisBJ AZitkVqE…QvKnvXNa

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.

1.536 × 10¹⁰³(104-digit number)

15364678800608251946…45148720041246784959

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

1.536 × 10¹⁰³(104-digit number)

15364678800608251946…45148720041246784959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.536 × 10¹⁰³(104-digit number)

15364678800608251946…45148720041246784961

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

3.072 × 10¹⁰³(104-digit number)

30729357601216503892…90297440082493569919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.072 × 10¹⁰³(104-digit number)

30729357601216503892…90297440082493569921

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

6.145 × 10¹⁰³(104-digit number)

61458715202433007784…80594880164987139839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.145 × 10¹⁰³(104-digit number)

61458715202433007784…80594880164987139841

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

1.229 × 10¹⁰⁴(105-digit number)

12291743040486601556…61189760329974279679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.229 × 10¹⁰⁴(105-digit number)

12291743040486601556…61189760329974279681

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

2.458 × 10¹⁰⁴(105-digit number)

24583486080973203113…22379520659948559359

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