Block #476,531

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/5/2014, 9:40:16 PM · Difficulty 10.4732 · 6,313,544 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8ff1d61eb50c5042112b3dcaf7f0b1cef423e0d49ab9500f5142ec62a803ed18

View on Chainz ↗

Height

#476,531

Difficulty

10.473248

Transactions

Size

880 B

Version

Bits

0a7926c0

Nonce

12,267

Timestamp

4/5/2014, 9:40:16 PM

Confirmations

6,313,544

Merkle Root

4777ab4cdc0d4197e4e8b17efb5c8d5349be9f0db30df146755749b376838d49

Transactions (4)

Coinbaseaa923d5acf278c…95adb75877761a

1 in → 1 out9.1300 XPM110 B

AeKNrjNj…1NEq95Ta

50312193efc8e1…09192441ae527f

1 in → 2 out6.5842 XPM224 B

AKeVHE5u…GN1y5WWE AKUjo9Co…52LBc49t

45b06244f4f11d…a24ba6aa94c291

1 in → 2 out3.5611 XPM226 B

AdMqaa4c…4kYj35TU AHLWVEo6…wcqXevSs

1189aa83889adb…8d39de44cc0ca0

1 in → 2 out2.5148 XPM227 B

AeDFWfLr…ocqM5DJT AUGi6Fmm…kvFR5Srp

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.

6.642 × 10¹⁰¹(102-digit number)

66422792091739964643…63557441151276297599

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

6.642 × 10¹⁰¹(102-digit number)

66422792091739964643…63557441151276297599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.642 × 10¹⁰¹(102-digit number)

66422792091739964643…63557441151276297601

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

1.328 × 10¹⁰²(103-digit number)

13284558418347992928…27114882302552595199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.328 × 10¹⁰²(103-digit number)

13284558418347992928…27114882302552595201

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

2.656 × 10¹⁰²(103-digit number)

26569116836695985857…54229764605105190399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.656 × 10¹⁰²(103-digit number)

26569116836695985857…54229764605105190401

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

5.313 × 10¹⁰²(103-digit number)

53138233673391971715…08459529210210380799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.313 × 10¹⁰²(103-digit number)

53138233673391971715…08459529210210380801

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

1.062 × 10¹⁰³(104-digit number)

10627646734678394343…16919058420420761599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.062 × 10¹⁰³(104-digit number)

10627646734678394343…16919058420420761601

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.125 × 10¹⁰³(104-digit number)

21255293469356788686…33838116840841523199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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