Block #216,465

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/18/2013, 6:14:27 PM · Difficulty 9.9266 · 6,589,259 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ee56c15b311a60d5d9b1bdf0b53132d808fbb42788136fd5b61d9a73c3431106

View on Chainz ↗

Height

#216,465

Difficulty

9.926621

Transactions

Size

1.24 KB

Version

Bits

09ed370f

Nonce

65,846

Timestamp

10/18/2013, 6:14:27 PM

Confirmations

6,589,259

Mined by

⛏️ MRaxAeNjg8HA2JzrdQD3LcJMTkwYEE9AkdpcSC

Merkle Root

8c50fcb4cbfb26b4e69477de88434ca91a1171d481729d1b564591fdceed80c4

Transactions (1)

Coinbase8c50fcb4cbfb26…4591fdceed80c4

1 in → 33 out10.1100 XPM1.16 KB

AeNjg8HA…9AkdpcSC AbeUZSvK…ijGzuyjz AKXeSXzu…yeuNjvhB AKFBsJ1Y…LYyU7TbU ARpndEmc…Hg792kEk

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.

6.439 × 10⁹⁴(95-digit number)

64393903203595393805…95345349662017790079

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

6.439 × 10⁹⁴(95-digit number)

64393903203595393805…95345349662017790079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.439 × 10⁹⁴(95-digit number)

64393903203595393805…95345349662017790081

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

1.287 × 10⁹⁵(96-digit number)

12878780640719078761…90690699324035580159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.287 × 10⁹⁵(96-digit number)

12878780640719078761…90690699324035580161

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

2.575 × 10⁹⁵(96-digit number)

25757561281438157522…81381398648071160319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.575 × 10⁹⁵(96-digit number)

25757561281438157522…81381398648071160321

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

5.151 × 10⁹⁵(96-digit number)

51515122562876315044…62762797296142320639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.151 × 10⁹⁵(96-digit number)

51515122562876315044…62762797296142320641

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

1.030 × 10⁹⁶(97-digit number)

10303024512575263008…25525594592284641279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.030 × 10⁹⁶(97-digit number)

10303024512575263008…25525594592284641281

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