Block #2,213,336

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/19/2017, 10:45:53 AM · Difficulty 10.9441 · 4,612,990 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e25320d10df2148ee90c57e47313ed4b4e4f13f66fa83693f7e0290711728f44

View on Chainz ↗

Height

#2,213,336

Difficulty

10.944056

Transactions

Size

427 B

Version

Bits

0af1ada8

Nonce

1,366,327,925

Timestamp

7/19/2017, 10:45:53 AM

Confirmations

4,612,990

Mined by

⛏️ P2SHAFzt7kKr4Z6LPLDgEuGxqMBuXTYSkUHggQ

Merkle Root

4cf1f12decc9622ba8cb6fa815d8f5a7d23a745ba210a405ca2003e488ef6a3f

Transactions (2)

Coinbase5539111a333126…22c254668bd2df

1 in → 1 out8.3500 XPM110 B

AFzt7kKr…YSkUHggQ

0cbbcfd1def403…1aab3733bab191

1 in → 2 out98153.9007 XPM226 B

AccGZuG7…uDYvEMyD AJySnNqu…3adXwvuc

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.

4.338 × 10⁹⁷(98-digit number)

43389557284908104589…26132183612728606719

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

4.338 × 10⁹⁷(98-digit number)

43389557284908104589…26132183612728606719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.338 × 10⁹⁷(98-digit number)

43389557284908104589…26132183612728606721

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

8.677 × 10⁹⁷(98-digit number)

86779114569816209179…52264367225457213439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.677 × 10⁹⁷(98-digit number)

86779114569816209179…52264367225457213441

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

1.735 × 10⁹⁸(99-digit number)

17355822913963241835…04528734450914426879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.735 × 10⁹⁸(99-digit number)

17355822913963241835…04528734450914426881

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

3.471 × 10⁹⁸(99-digit number)

34711645827926483671…09057468901828853759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.471 × 10⁹⁸(99-digit number)

34711645827926483671…09057468901828853761

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

6.942 × 10⁹⁸(99-digit number)

69423291655852967343…18114937803657707519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.942 × 10⁹⁸(99-digit number)

69423291655852967343…18114937803657707521

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 #2,213,336

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