Block #536,510

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/11/2014, 10:53:35 AM · Difficulty 10.9105 · 6,270,131 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3c2552a229e13cadab02b6b4c30f5d1605a30fb4c1f75bac9cfc5a26cd6cb9d5

View on Chainz ↗

Height

#536,510

Difficulty

10.910517

Transactions

Size

835 B

Version

Bits

0ae9179e

Nonce

7,449

Timestamp

5/11/2014, 10:53:35 AM

Confirmations

6,270,131

Mined by

⛏️ qAGz9gyZWgxBxAyVrKrWDzMw21kbo8NYQpw

Merkle Root

2ec6899bccf9f28cca3d1c894f3f35c63c053c305626519710764062028a5e76

Transactions (1)

Coinbase2ec6899bccf9f2…764062028a5e76

1 in → 20 out8.3900 XPM743 B

AGz9gyZW…bo8NYQpw AbHY4iza…Yckt2J5W AbPcCMg4…719q6mAX AUFKXvnz…342ApNcm ATp4jJhs…TbSgR8Qb

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.

4.925 × 10¹⁰⁰(101-digit number)

49251166278431484202…07334122522883167439

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

4.925 × 10¹⁰⁰(101-digit number)

49251166278431484202…07334122522883167439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.925 × 10¹⁰⁰(101-digit number)

49251166278431484202…07334122522883167441

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

9.850 × 10¹⁰⁰(101-digit number)

98502332556862968404…14668245045766334879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.850 × 10¹⁰⁰(101-digit number)

98502332556862968404…14668245045766334881

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

1.970 × 10¹⁰¹(102-digit number)

19700466511372593680…29336490091532669759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.970 × 10¹⁰¹(102-digit number)

19700466511372593680…29336490091532669761

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

3.940 × 10¹⁰¹(102-digit number)

39400933022745187361…58672980183065339519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.940 × 10¹⁰¹(102-digit number)

39400933022745187361…58672980183065339521

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

7.880 × 10¹⁰¹(102-digit number)

78801866045490374723…17345960366130679039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.880 × 10¹⁰¹(102-digit number)

78801866045490374723…17345960366130679041

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 #536,510

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