Block #327,494

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/24/2013, 2:20:46 PM · Difficulty 10.1771 · 6,475,790 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8275245665ddfc49fba7f37013d38dcaa666c9e529ea12945ae98db3ef6c9b18

View on Chainz ↗

Height

#327,494

Difficulty

10.177123

Transactions

Size

832 B

Version

Bits

0a2d57ef

Nonce

4,389

Timestamp

12/24/2013, 2:20:46 PM

Confirmations

6,475,790

Mined by

⛏️ FaRAKxxLGqhSp8N6q1niks6PPt79QoySJc6b5

Merkle Root

b18325a6cde41dab1879d3b6b682fa1851231920b2bfa97567e47a635e913820

Transactions (4)

Coinbase7d777f1d108e51…5c27a97e8c234c

1 in → 1 out9.6400 XPM97 B

AKxxLGqh…oySJc6b5

4e5f9489dadf7c…648338275381ab

1 in → 2 out9.7300 XPM192 B

Ab1S9WmV…AdS8hG2Z AUNWWMCz…rmrt9pxA

e7e59b2955b96b…630eb31952d24d

1 in → 2 out5.4645 XPM227 B

APzjsAj1…khwiuKXY Ad9TBBom…9GBvhp35

6f6c44a186d274…56913e1f0f8418

1 in → 2 out2.5342 XPM226 B

ARU1jarz…PssrKtXM ATRRztAY…PfsMwTxb

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.

3.979 × 10⁹⁴(95-digit number)

39794702427309226236…36979017764666560639

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

3.979 × 10⁹⁴(95-digit number)

39794702427309226236…36979017764666560639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.979 × 10⁹⁴(95-digit number)

39794702427309226236…36979017764666560641

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

7.958 × 10⁹⁴(95-digit number)

79589404854618452473…73958035529333121279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.958 × 10⁹⁴(95-digit number)

79589404854618452473…73958035529333121281

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

1.591 × 10⁹⁵(96-digit number)

15917880970923690494…47916071058666242559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.591 × 10⁹⁵(96-digit number)

15917880970923690494…47916071058666242561

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

3.183 × 10⁹⁵(96-digit number)

31835761941847380989…95832142117332485119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.183 × 10⁹⁵(96-digit number)

31835761941847380989…95832142117332485121

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

6.367 × 10⁹⁵(96-digit number)

63671523883694761978…91664284234664970239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.367 × 10⁹⁵(96-digit number)

63671523883694761978…91664284234664970241

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