Block #497,963

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/17/2014, 8:46:21 PM · Difficulty 10.7743 · 6,311,747 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

34cd0cb7fff0cb2063c77ac4ac292bbf6a3c51919b9b4b3a429e53bff0cb1d10

View on Chainz ↗

Height

#497,963

Difficulty

10.774279

Transactions

Size

1.44 KB

Version

Bits

0ac63726

Nonce

403,393,936

Timestamp

4/17/2014, 8:46:21 PM

Confirmations

6,311,747

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

895651faf2166295f4402ae7a9beaf307f874b31d26fe7e1a93ea946a6b9970e

Transactions (2)

Coinbased15f046fd140be…7699c8eda672c8

1 in → 1 out8.6200 XPM116 B

AbwWkWZt…kawDhufa

1a3c72cf1cab28…500b65734bbeaf

8 in → 2 out1800.0000 XPM1.24 KB

ATm8Cdf9…ZZGqGLHs AM2VvvW9…FiFGXpMG

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.

7.818 × 10⁹⁸(99-digit number)

78189388095929174211…21792729511114919679

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

7.818 × 10⁹⁸(99-digit number)

78189388095929174211…21792729511114919679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.818 × 10⁹⁸(99-digit number)

78189388095929174211…21792729511114919681

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

1.563 × 10⁹⁹(100-digit number)

15637877619185834842…43585459022229839359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.563 × 10⁹⁹(100-digit number)

15637877619185834842…43585459022229839361

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

3.127 × 10⁹⁹(100-digit number)

31275755238371669684…87170918044459678719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.127 × 10⁹⁹(100-digit number)

31275755238371669684…87170918044459678721

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

6.255 × 10⁹⁹(100-digit number)

62551510476743339369…74341836088919357439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.255 × 10⁹⁹(100-digit number)

62551510476743339369…74341836088919357441

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

1.251 × 10¹⁰⁰(101-digit number)

12510302095348667873…48683672177838714879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.251 × 10¹⁰⁰(101-digit number)

12510302095348667873…48683672177838714881

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 #497,963

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