Block #310,295

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/14/2013, 12:05:30 AM · Difficulty 9.9951 · 6,496,671 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8c7905fa6f2d4113684f3ed88c4d1962f341cf4dbd658f98a9577302e50ec715

View on Chainz ↗

Height

#310,295

Difficulty

9.995134

Transactions

Size

1.01 KB

Version

Bits

09fec117

Nonce

129,063

Timestamp

12/14/2013, 12:05:30 AM

Confirmations

6,496,671

Mined by

⛏️ aRAYtDvcGsMH2GY5bD4Hc2rArhMdVuAcA7m7

Merkle Root

282eaab11271b74d620acf3083e0ee8fef18db4bf491ee4c518d6233a398734c

Transactions (1)

Coinbase282eaab11271b7…8d6233a398734c

1 in → 26 out9.9900 XPM947 B

AYtDvcGs…VuAcA7m7 Aac9Hjdg…P4ktypc3 AbtgNzNb…9Atvu81w Ad9pSzHt…cpJ3y2zz AKvZtqvQ…V41oFZs7

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.

2.447 × 10⁹⁷(98-digit number)

24472657292516439101…67896276086643510999

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

2.447 × 10⁹⁷(98-digit number)

24472657292516439101…67896276086643510999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.447 × 10⁹⁷(98-digit number)

24472657292516439101…67896276086643511001

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

4.894 × 10⁹⁷(98-digit number)

48945314585032878202…35792552173287021999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.894 × 10⁹⁷(98-digit number)

48945314585032878202…35792552173287022001

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

9.789 × 10⁹⁷(98-digit number)

97890629170065756404…71585104346574043999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.789 × 10⁹⁷(98-digit number)

97890629170065756404…71585104346574044001

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

1.957 × 10⁹⁸(99-digit number)

19578125834013151280…43170208693148087999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.957 × 10⁹⁸(99-digit number)

19578125834013151280…43170208693148088001

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

3.915 × 10⁹⁸(99-digit number)

39156251668026302561…86340417386296175999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.915 × 10⁹⁸(99-digit number)

39156251668026302561…86340417386296176001

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

Block #310,295

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