Block #216,087

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/18/2013, 1:08:01 PM · Difficulty 9.9255 · 6,578,403 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9ef06af80f102b3879c5ab5115b69e5bfb7a7f77b6539a650088e96eb4f70d71

View on Chainz ↗

Height

#216,087

Difficulty

9.925490

Transactions

Size

1.90 KB

Version

Bits

09ecece6

Nonce

138,716

Timestamp

10/18/2013, 1:08:01 PM

Confirmations

6,578,403

Mined by

⛏️ P2SHARZhTvuqKB14YYGXzMsrhzejN23yv9P7i3

Merkle Root

94e95fa5e1acb4ebd43f284f1e3fb0323c9458f3f4eab69f280614f19b105af6

Transactions (3)

Coinbase80af7efb4511fe…32e35968542b1b

1 in → 1 out10.1700 XPM109 B

ARZhTvuq…3yv9P7i3

4323de8e7f436d…355e3163d342bc

3 in → 1 out2994.0000 XPM487 B

AM1KSTkC…iVmrUJqw

4a6dd5bcb49fef…afcd4cf341f9f5

8 in → 2 out298.9592 XPM1.23 KB

AFnknN5w…uNvnyk7C AKcwruc8…XhAGZ5iV

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.

2.551 × 10⁹³(94-digit number)

25510842759566356277…32293049721222768319

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

2.551 × 10⁹³(94-digit number)

25510842759566356277…32293049721222768319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.551 × 10⁹³(94-digit number)

25510842759566356277…32293049721222768321

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

5.102 × 10⁹³(94-digit number)

51021685519132712554…64586099442445536639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.102 × 10⁹³(94-digit number)

51021685519132712554…64586099442445536641

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

1.020 × 10⁹⁴(95-digit number)

10204337103826542510…29172198884891073279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.020 × 10⁹⁴(95-digit number)

10204337103826542510…29172198884891073281

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

2.040 × 10⁹⁴(95-digit number)

20408674207653085021…58344397769782146559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.040 × 10⁹⁴(95-digit number)

20408674207653085021…58344397769782146561

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

4.081 × 10⁹⁴(95-digit number)

40817348415306170043…16688795539564293119

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