Block #1,225,320

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/7/2015, 2:06:22 AM · Difficulty 10.7364 · 5,568,969 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e2116ede2f789a9d9e2d7d8797d5a3cb036c87079dcad544daef58a9310073ce

View on Chainz ↗

Height

#1,225,320

Difficulty

10.736435

Transactions

Size

199 B

Version

Bits

0abc8700

Nonce

1,316,553,512

Timestamp

9/7/2015, 2:06:22 AM

Confirmations

5,568,969

Merkle Root

ab679e407e8569a12f4b3189103b045da7da9538819f88a43e07f3dabc6d6571

Transactions (1)

Coinbaseab679e407e8569…07f3dabc6d6571

1 in → 1 out8.6600 XPM109 B

ALUDpg5V…nHDRNGFJ

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.

5.326 × 10⁹⁵(96-digit number)

53260311560422994152…53826854766128655999

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

5.326 × 10⁹⁵(96-digit number)

53260311560422994152…53826854766128655999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.326 × 10⁹⁵(96-digit number)

53260311560422994152…53826854766128656001

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

1.065 × 10⁹⁶(97-digit number)

10652062312084598830…07653709532257311999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.065 × 10⁹⁶(97-digit number)

10652062312084598830…07653709532257312001

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

2.130 × 10⁹⁶(97-digit number)

21304124624169197661…15307419064514623999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.130 × 10⁹⁶(97-digit number)

21304124624169197661…15307419064514624001

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

4.260 × 10⁹⁶(97-digit number)

42608249248338395322…30614838129029247999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.260 × 10⁹⁶(97-digit number)

42608249248338395322…30614838129029248001

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

8.521 × 10⁹⁶(97-digit number)

85216498496676790644…61229676258058495999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.521 × 10⁹⁶(97-digit number)

85216498496676790644…61229676258058496001

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