Block #220,087

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/20/2013, 8:06:55 PM · Difficulty 9.9353 · 6,572,954 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9f3c0cc649492d0c432fa445360ea8dfda07a20e85247243d68b5df9c41baf0f

View on Chainz ↗

Height

#220,087

Difficulty

9.935348

Transactions

Size

652 B

Version

Bits

09ef72f5

Nonce

89,785

Timestamp

10/20/2013, 8:06:55 PM

Confirmations

6,572,954

Merkle Root

e8dd68cbefdbcd5d86354a661c09b8ef0213a350096c24228402102edf9ba3b5

Transactions (3)

Coinbaseb8f713c34fa594…561c0e11658f3f

1 in → 1 out10.1400 XPM109 B

AZwW64La…vRL3iYk4

31d361672ed410…7471062118cd24

1 in → 2 out8.3494 XPM226 B

AW3EmRaE…XUXzstGP AcMA4cjS…zP22nBSS

e8e223af1f57e2…a8f35a06d8a219

1 in → 2 out8.1043 XPM227 B

ARUsiQv5…XstdNDkW AH3dDrPX…iXBYe8ZV

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.

5.248 × 10⁹³(94-digit number)

52486430617725458373…25909919518888892799

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

5.248 × 10⁹³(94-digit number)

52486430617725458373…25909919518888892799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.248 × 10⁹³(94-digit number)

52486430617725458373…25909919518888892801

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

1.049 × 10⁹⁴(95-digit number)

10497286123545091674…51819839037777785599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.049 × 10⁹⁴(95-digit number)

10497286123545091674…51819839037777785601

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

2.099 × 10⁹⁴(95-digit number)

20994572247090183349…03639678075555571199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.099 × 10⁹⁴(95-digit number)

20994572247090183349…03639678075555571201

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

4.198 × 10⁹⁴(95-digit number)

41989144494180366698…07279356151111142399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.198 × 10⁹⁴(95-digit number)

41989144494180366698…07279356151111142401

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

8.397 × 10⁹⁴(95-digit number)

83978288988360733396…14558712302222284799

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