Block #81,366

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/24/2013, 5:11:40 PM · Difficulty 9.2695 · 6,713,396 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

67ad3c58cd2866b055f1ab11dc5d92f8941b3cf81006e34a35c4c4ea092e390c

View on Chainz ↗

Height

#81,366

Difficulty

9.269490

Transactions

Size

719 B

Version

Bits

0944fd4f

Nonce

319

Timestamp

7/24/2013, 5:11:40 PM

Confirmations

6,713,396

Mined by

⛏️ P2SHAQUECDFyDsrCu9L4pBSAno8HTgnrepQg8L

Merkle Root

8332c745a6695c8afcb16f791937ea04e14dbf9e9f347b728b91171866bc8403

Transactions (2)

Coinbase53c8b795603dad…4b6ff6171b8904

1 in → 1 out11.6300 XPM109 B

AQUECDFy…nrepQg8L

8c7629be732a9a…3652737e49536d

3 in → 2 out1.0138 XPM521 B

ATXuY4KL…dvCnw78e AUZMAUgc…puKWvjtP

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.

4.014 × 10⁹¹(92-digit number)

40144037516396025906…58996988873361915579

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

4.014 × 10⁹¹(92-digit number)

40144037516396025906…58996988873361915579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.014 × 10⁹¹(92-digit number)

40144037516396025906…58996988873361915581

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

8.028 × 10⁹¹(92-digit number)

80288075032792051813…17993977746723831159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.028 × 10⁹¹(92-digit number)

80288075032792051813…17993977746723831161

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

1.605 × 10⁹²(93-digit number)

16057615006558410362…35987955493447662319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.605 × 10⁹²(93-digit number)

16057615006558410362…35987955493447662321

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

3.211 × 10⁹²(93-digit number)

32115230013116820725…71975910986895324639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.211 × 10⁹²(93-digit number)

32115230013116820725…71975910986895324641

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

6.423 × 10⁹²(93-digit number)

64230460026233641451…43951821973790649279

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