Block #497,806

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/17/2014, 6:50:21 PM · Difficulty 10.7724 · 6,309,163 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

acee9151f135801751d15607dee173ec0328215ae7b2de0ae4f0f1f5d26c4413

View on Chainz ↗

Height

#497,806

Difficulty

10.772372

Transactions

Size

400 B

Version

Bits

0ac5ba34

Nonce

19,567,734

Timestamp

4/17/2014, 6:50:21 PM

Confirmations

6,309,163

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

766579837f55f15b911caa17a7349d5f29d147c3c07be6f2eecbbb22911fcd3f

Transactions (2)

Coinbasebbacee14481c55…2e2a21ab3971e0

1 in → 1 out8.6100 XPM116 B

AbwWkWZt…kawDhufa

3bf234c589d59c…7ce4c17ae1d42c

1 in → 1 out2.9939 XPM193 B

AXCNJAvq…qsPtg17V

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.

4.229 × 10⁹⁷(98-digit number)

42295015285225813798…23338509375146870919

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

4.229 × 10⁹⁷(98-digit number)

42295015285225813798…23338509375146870919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.229 × 10⁹⁷(98-digit number)

42295015285225813798…23338509375146870921

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

8.459 × 10⁹⁷(98-digit number)

84590030570451627596…46677018750293741839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.459 × 10⁹⁷(98-digit number)

84590030570451627596…46677018750293741841

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

1.691 × 10⁹⁸(99-digit number)

16918006114090325519…93354037500587483679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.691 × 10⁹⁸(99-digit number)

16918006114090325519…93354037500587483681

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

3.383 × 10⁹⁸(99-digit number)

33836012228180651038…86708075001174967359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.383 × 10⁹⁸(99-digit number)

33836012228180651038…86708075001174967361

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

6.767 × 10⁹⁸(99-digit number)

67672024456361302077…73416150002349934719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.767 × 10⁹⁸(99-digit number)

67672024456361302077…73416150002349934721

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 #497,806

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