Block #215,810

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/18/2013, 8:31:37 AM · Difficulty 9.9255 · 6,583,196 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1b1445aa5507be00988f43cfead2609988c64ab4df3e38ab2fc4a19830669027

View on Chainz ↗

Height

#215,810

Difficulty

9.925453

Transactions

Size

6.46 KB

Version

Bits

09ecea7a

Nonce

52,696

Timestamp

10/18/2013, 8:31:37 AM

Confirmations

6,583,196

Mined by

⛏️ KR`AckGXHgeUDAjFoqBtT1MAmBNeDbkNJhGsA

Merkle Root

b1b3ce2b7f37ac14a69430f44e24a923c2d7e872df8a9f4838853ac58dc0a1fd

Transactions (1)

Coinbaseb1b3ce2b7f37ac…853ac58dc0a1fd

1 in → 190 out10.0700 XPM6.37 KB

AckGXHge…bkNJhGsA AQqSxkMw…QBRoAg6B AXJbpPXX…UowxmF1S ASGXhVnp…gHNxHQYB AGaKkABV…XGSDBNzn

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.

6.075 × 10⁹¹(92-digit number)

60758321140886994528…20227934688908307799

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

6.075 × 10⁹¹(92-digit number)

60758321140886994528…20227934688908307799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.075 × 10⁹¹(92-digit number)

60758321140886994528…20227934688908307801

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

1.215 × 10⁹²(93-digit number)

12151664228177398905…40455869377816615599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.215 × 10⁹²(93-digit number)

12151664228177398905…40455869377816615601

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

2.430 × 10⁹²(93-digit number)

24303328456354797811…80911738755633231199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.430 × 10⁹²(93-digit number)

24303328456354797811…80911738755633231201

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

4.860 × 10⁹²(93-digit number)

48606656912709595622…61823477511266462399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.860 × 10⁹²(93-digit number)

48606656912709595622…61823477511266462401

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

9.721 × 10⁹²(93-digit number)

97213313825419191245…23646955022532924799

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