Block #287,841

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/1/2013, 12:01:14 PM · Difficulty 9.9871 · 6,511,514 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0c627e2cb7e038472eec7609dfbc1be0dab4f77ab54c6fb78017a245d5fb6d81

View on Chainz ↗

Height

#287,841

Difficulty

9.987092

Transactions

Size

1.02 KB

Version

Bits

09fcb208

Nonce

15,210

Timestamp

12/1/2013, 12:01:14 PM

Confirmations

6,511,514

Mined by

⛏️ adaR%ATekAd27GiyEw51TeYVJABha8AWYWxPoh7

Merkle Root

c47596e77c780fb458d27cebe9f6814e64bf08a4d590c4ea403a05c7b07bbaac

Transactions (2)

Coinbaseb238e719d39917…402c3575d784cb

1 in → 2 out10.0100 XPM131 B

ATekAd27…WYWxPoh7 AJiK61PW…4iisLqYP

42553e04239b8f…951db5a621c74f

5 in → 2 out509.1897 XPM821 B

AV1q7Lhu…MgVTmBzX ANBtmnPD…QJyEku9c

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.

2.208 × 10⁹¹(92-digit number)

22087178584812910786…23993394494053286719

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

2.208 × 10⁹¹(92-digit number)

22087178584812910786…23993394494053286719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.208 × 10⁹¹(92-digit number)

22087178584812910786…23993394494053286721

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

4.417 × 10⁹¹(92-digit number)

44174357169625821572…47986788988106573439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.417 × 10⁹¹(92-digit number)

44174357169625821572…47986788988106573441

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

8.834 × 10⁹¹(92-digit number)

88348714339251643145…95973577976213146879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.834 × 10⁹¹(92-digit number)

88348714339251643145…95973577976213146881

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

1.766 × 10⁹²(93-digit number)

17669742867850328629…91947155952426293759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.766 × 10⁹²(93-digit number)

17669742867850328629…91947155952426293761

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

3.533 × 10⁹²(93-digit number)

35339485735700657258…83894311904852587519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.533 × 10⁹²(93-digit number)

35339485735700657258…83894311904852587521

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