Block #287,179

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/1/2013, 5:19:47 AM · Difficulty 9.9864 · 6,507,858 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

359ace4a81fa13e2065999a7ca4bdfe3275cca41916e17dca8f1ac73b7b369e9

View on Chainz ↗

Height

#287,179

Difficulty

9.986387

Transactions

Size

2.28 KB

Version

Bits

09fc83df

Nonce

46,836

Timestamp

12/1/2013, 5:19:47 AM

Confirmations

6,507,858

Mined by

⛏️ aaRAYcLTeXRXcXHePDnP5p1bevW8AbscgPops

Merkle Root

57bf1e337d9e124de258d6e18789eaa08cadcf6c7fd81b61a25bca0e6ef46d23

Transactions (2)

Coinbase1e77a433281bce…520e27f5389386

1 in → 27 out10.0100 XPM981 B

AYcLTeXR…bscgPops AV6uuy6Z…MwQRdBX5 ARUF4w2c…FUVpAWxv AGFAJ5YL…ZEnBbk6G ANkX1YyE…kHwVW1hd

5a540c51d41c1f…1a3af3813f5962

8 in → 2 out80.1759 XPM1.23 KB

ATs7Rkry…sDeQuaNH AdFUuvzN…1uTXhrtF

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.

1.833 × 10⁹³(94-digit number)

18338592933466740906…84840276256603239039

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

1.833 × 10⁹³(94-digit number)

18338592933466740906…84840276256603239039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.833 × 10⁹³(94-digit number)

18338592933466740906…84840276256603239041

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

3.667 × 10⁹³(94-digit number)

36677185866933481813…69680552513206478079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.667 × 10⁹³(94-digit number)

36677185866933481813…69680552513206478081

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

7.335 × 10⁹³(94-digit number)

73354371733866963627…39361105026412956159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.335 × 10⁹³(94-digit number)

73354371733866963627…39361105026412956161

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

1.467 × 10⁹⁴(95-digit number)

14670874346773392725…78722210052825912319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.467 × 10⁹⁴(95-digit number)

14670874346773392725…78722210052825912321

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

2.934 × 10⁹⁴(95-digit number)

29341748693546785450…57444420105651824639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.934 × 10⁹⁴(95-digit number)

29341748693546785450…57444420105651824641

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