Block #471,205

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/2/2014, 10:47:05 AM · Difficulty 10.4314 · 6,346,567 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a4305d038bdc7d2e877fd1cf7d51f27ec1c846e41d79fb76dd8f06e518767228

View on Chainz ↗

Height

#471,205

Difficulty

10.431400

Transactions

Size

1.52 KB

Version

Bits

0a6e7035

Nonce

239,864

Timestamp

4/2/2014, 10:47:05 AM

Confirmations

6,346,567

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

9cfa94f1f4b0268cc2fbddadecb7d0033448a4e0abb021737581c376867384bc

Transactions (2)

Coinbase1c79e799312e79…49ce8596624077

1 in → 21 out9.1900 XPM777 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AUzEPJFG…kYkA5U9V ATp4jJhs…TbSgR8Qb Adbb4svj…dQWTHsq5

79611b99d4f6ab…ecc05f675508c5

3 in → 10 out27.5500 XPM691 B

AGpWgeTP…pYX3F9ug AeKNrjNj…1NEq95Ta ALyNEVRS…TiuPe2AM AUA3VCcz…bSHFyasf ALbMSCr6…Nv7gDkZj

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.

1.520 × 10⁹⁷(98-digit number)

15209008153284852354…34254905628422520959

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

1.520 × 10⁹⁷(98-digit number)

15209008153284852354…34254905628422520959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.520 × 10⁹⁷(98-digit number)

15209008153284852354…34254905628422520961

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

3.041 × 10⁹⁷(98-digit number)

30418016306569704708…68509811256845041919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.041 × 10⁹⁷(98-digit number)

30418016306569704708…68509811256845041921

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

6.083 × 10⁹⁷(98-digit number)

60836032613139409416…37019622513690083839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.083 × 10⁹⁷(98-digit number)

60836032613139409416…37019622513690083841

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

1.216 × 10⁹⁸(99-digit number)

12167206522627881883…74039245027380167679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.216 × 10⁹⁸(99-digit number)

12167206522627881883…74039245027380167681

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

2.433 × 10⁹⁸(99-digit number)

24334413045255763766…48078490054760335359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.433 × 10⁹⁸(99-digit number)

24334413045255763766…48078490054760335361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #471,205

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