Block #222,183

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/22/2013, 1:09:03 AM · Difficulty 9.9399 · 6,595,537 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5087ea9406b47ae45b10a6db5a8840f9cede979a35feb601f63e571070a03e06

View on Chainz ↗

Height

#222,183

Difficulty

9.939865

Transactions

Size

2.01 KB

Version

Bits

09f09af7

Nonce

371,736

Timestamp

10/22/2013, 1:09:03 AM

Confirmations

6,595,537

Mined by

⛏️ cReXAG3pF3b676H4WMjMV7hee7ax51xMVHvzda

Merkle Root

705fa45fa09cc77b3d674304716000a4b2c9dbedb14780dc8d0b918ee1b0218e

Transactions (2)

Coinbase40deee79f2f1bf…a0ba352cae8771

1 in → 45 out10.0900 XPM1.55 KB

AG3pF3b6…xMVHvzda Aaox8Rxx…XTyyJXVx ARpndEmc…Hg792kEk AJKYzp1g…SvZiepke AScCYXya…oAz38X3p

a81d2b7de7b988…2b260d7e7cc312

2 in → 2 out10.3409 XPM375 B

AHyHEeYQ…XuELsExj AVDum9wm…xrB56LGB

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.

8.623 × 10⁹⁵(96-digit number)

86233408919888184494…22951581881123841919

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

8.623 × 10⁹⁵(96-digit number)

86233408919888184494…22951581881123841919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.623 × 10⁹⁵(96-digit number)

86233408919888184494…22951581881123841921

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

1.724 × 10⁹⁶(97-digit number)

17246681783977636898…45903163762247683839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.724 × 10⁹⁶(97-digit number)

17246681783977636898…45903163762247683841

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

3.449 × 10⁹⁶(97-digit number)

34493363567955273797…91806327524495367679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.449 × 10⁹⁶(97-digit number)

34493363567955273797…91806327524495367681

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

6.898 × 10⁹⁶(97-digit number)

68986727135910547595…83612655048990735359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.898 × 10⁹⁶(97-digit number)

68986727135910547595…83612655048990735361

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

1.379 × 10⁹⁷(98-digit number)

13797345427182109519…67225310097981470719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #222,183

Cookie Preferences