Block #1,320,968

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/10/2015, 8:57:54 AM · Difficulty 10.8594 · 5,488,648 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

507e56320f497b12db98c600dc7546ddc60b52895b52d1e32aa16013e4fb2642

View on Chainz ↗

Height

#1,320,968

Difficulty

10.859412

Transactions

Size

14.87 KB

Version

Bits

0adc0271

Nonce

1,122,942,535

Timestamp

11/10/2015, 8:57:54 AM

Confirmations

5,488,648

Mined by

⛏️ P2SHALyz7LENQHkBaSSaRaUmVKsVudWkyWJyRG

Merkle Root

089d44fe6b8bd55dcbab8ebd375d5c599c3761d1563d45501d188daf5bf4e173

Transactions (2)

Coinbasea3ae9e64f6d44f…5380927f321871

1 in → 1 out8.6400 XPM110 B

ALyz7LEN…WkyWJyRG

9b152d524997aa…0e194bf6e0aceb

101 in → 2 out500.0100 XPM14.67 KB

AJjnK9uC…VreFquR4 AY3EWgVJ…EXUBh8t7

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.

3.085 × 10⁹⁶(97-digit number)

30858565437374448942…23892163403427061759

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

3.085 × 10⁹⁶(97-digit number)

30858565437374448942…23892163403427061759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.085 × 10⁹⁶(97-digit number)

30858565437374448942…23892163403427061761

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

6.171 × 10⁹⁶(97-digit number)

61717130874748897884…47784326806854123519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.171 × 10⁹⁶(97-digit number)

61717130874748897884…47784326806854123521

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

1.234 × 10⁹⁷(98-digit number)

12343426174949779576…95568653613708247039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.234 × 10⁹⁷(98-digit number)

12343426174949779576…95568653613708247041

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

2.468 × 10⁹⁷(98-digit number)

24686852349899559153…91137307227416494079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.468 × 10⁹⁷(98-digit number)

24686852349899559153…91137307227416494081

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

4.937 × 10⁹⁷(98-digit number)

49373704699799118307…82274614454832988159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.937 × 10⁹⁷(98-digit number)

49373704699799118307…82274614454832988161

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 #1,320,968

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