Block #220,678

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/21/2013, 3:48:33 AM · Difficulty 9.9370 · 6,575,466 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c4610d9741eaa87f9f7c50d8374687abedd45919192cde850acf963ec9eb62cf

View on Chainz ↗

Height

#220,678

Difficulty

9.937045

Transactions

Size

2.76 KB

Version

Bits

09efe228

Nonce

94,952

Timestamp

10/21/2013, 3:48:33 AM

Confirmations

6,575,466

Mined by

⛏️ ^RdAeckU1KqT9KE6dvrDGRnRcSPq8a9chH61d

Merkle Root

70751fe962d90ff7a32b82adc7d3f78be65b75883fa216abcc3408123b30f6f4

Transactions (4)

Coinbase53f69dcd0823de…a1e021b0028bb5

1 in → 41 out10.0900 XPM1.42 KB

AeckU1Kq…a9chH61d AbeUZSvK…ijGzuyjz AKXeSXzu…yeuNjvhB ARpndEmc…Hg792kEk AScCYXya…oAz38X3p

35b8f3b7f862c9…b6b8c7f69b4227

1 in → 1 out10.1300 XPM157 B

AcWWWPc4…NKmGSdQs

499a739d4334bb…1ba362aa0d0874

1 in → 2 out10.1200 XPM191 B

AFz9fXym…wh4UqpkL AHgodDzy…fcGQDk3P

98fe34ed7e0dab…cfbdd9663e0511

6 in → 3 out22.1062 XPM931 B

AbuU1HhS…JPwsJEbB ARTJCDz1…oJ6Hi1d9 AHLyZUb7…cHnQjZJ9

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.

5.790 × 10⁹³(94-digit number)

57905840259403411183…92373763949293747199

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

5.790 × 10⁹³(94-digit number)

57905840259403411183…92373763949293747199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.790 × 10⁹³(94-digit number)

57905840259403411183…92373763949293747201

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

1.158 × 10⁹⁴(95-digit number)

11581168051880682236…84747527898587494399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.158 × 10⁹⁴(95-digit number)

11581168051880682236…84747527898587494401

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

2.316 × 10⁹⁴(95-digit number)

23162336103761364473…69495055797174988799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.316 × 10⁹⁴(95-digit number)

23162336103761364473…69495055797174988801

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

4.632 × 10⁹⁴(95-digit number)

46324672207522728946…38990111594349977599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.632 × 10⁹⁴(95-digit number)

46324672207522728946…38990111594349977601

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

9.264 × 10⁹⁴(95-digit number)

92649344415045457893…77980223188699955199

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