Block #220,690

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/21/2013, 4:00:38 AM · Difficulty 9.9371 · 6,575,444 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

953695a6faa18c59b1cb37fa0a7aa791bdee601e96f62a8fa53b7cc31c230ba0

View on Chainz ↗

Height

#220,690

Difficulty

9.937107

Transactions

Size

12.52 KB

Version

Bits

09efe646

Nonce

48,323

Timestamp

10/21/2013, 4:00:38 AM

Confirmations

6,575,444

Mined by

⛏️ P2SHAbuU1HhSi58QcdzhwKqhpJiRG3JPwsJEbB

Merkle Root

7f62759f8c80004cbaac35785df3f3cb4cd1e8b7040f65920382daaf119466e6

Transactions (2)

Coinbase6540d30a505d69…c9c5e3786005d5

1 in → 1 out10.2475 XPM110 B

AbuU1HhS…JPwsJEbB

2309ee282125fb…e0f796af12a3ce

85 in → 1 out296.5900 XPM12.32 KB

AV6URp9C…SYeCgYBK

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.

6.414 × 10⁹⁵(96-digit number)

64143226975732261242…27114364972752899039

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

6.414 × 10⁹⁵(96-digit number)

64143226975732261242…27114364972752899039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.414 × 10⁹⁵(96-digit number)

64143226975732261242…27114364972752899041

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

1.282 × 10⁹⁶(97-digit number)

12828645395146452248…54228729945505798079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.282 × 10⁹⁶(97-digit number)

12828645395146452248…54228729945505798081

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

2.565 × 10⁹⁶(97-digit number)

25657290790292904496…08457459891011596159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.565 × 10⁹⁶(97-digit number)

25657290790292904496…08457459891011596161

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

5.131 × 10⁹⁶(97-digit number)

51314581580585808993…16914919782023192319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.131 × 10⁹⁶(97-digit number)

51314581580585808993…16914919782023192321

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

1.026 × 10⁹⁷(98-digit number)

10262916316117161798…33829839564046384639

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