Block #495,263

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/16/2014, 1:35:43 PM · Difficulty 10.7334 · 6,318,949 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

248a3ed4187abc679e9de03d5eb954fccccc87964702719b7b22d43178e0af56

View on Chainz ↗

Height

#495,263

Difficulty

10.733386

Transactions

Size

677 B

Version

Bits

0abbbf28

Nonce

43,012

Timestamp

4/16/2014, 1:35:43 PM

Confirmations

6,318,949

Mined by

⛏️ nAKUN1D7mcA4QwLGNyRvGmKSfchyVvTNUMM

Merkle Root

1b1b80d1115823d788995fb28dd5430d5eab4d83c341bb490bdd65685377d7ec

Transactions (3)

Coinbase45a642e3050d3e…56c823ebf90b30

1 in → 2 out8.6900 XPM131 B

AKUN1D7m…yVvTNUMM AcaoBAGZ…n7zfVgjk

22df8fbe569bd3…5bba5d00e2bb68

1 in → 2 out6.6139 XPM227 B

AVhh2xBe…nkFDbFe9 AaeCeFsQ…HrCzFJkF

742c602f29b291…4f802cddf24173

1 in → 2 out5.8201 XPM226 B

APGSmbys…AgJ2wN2s AdobpKjj…M9auVuzw

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.

4.039 × 10¹⁰¹(102-digit number)

40392825996347873936…54544932112450610039

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

4.039 × 10¹⁰¹(102-digit number)

40392825996347873936…54544932112450610039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.039 × 10¹⁰¹(102-digit number)

40392825996347873936…54544932112450610041

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

8.078 × 10¹⁰¹(102-digit number)

80785651992695747873…09089864224901220079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.078 × 10¹⁰¹(102-digit number)

80785651992695747873…09089864224901220081

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

1.615 × 10¹⁰²(103-digit number)

16157130398539149574…18179728449802440159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.615 × 10¹⁰²(103-digit number)

16157130398539149574…18179728449802440161

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

3.231 × 10¹⁰²(103-digit number)

32314260797078299149…36359456899604880319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.231 × 10¹⁰²(103-digit number)

32314260797078299149…36359456899604880321

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

6.462 × 10¹⁰²(103-digit number)

64628521594156598298…72718913799209760639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.462 × 10¹⁰²(103-digit number)

64628521594156598298…72718913799209760641

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 #495,263

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