Block #1,359,493

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/7/2015, 3:24:55 PM · Difficulty 10.8385 · 5,444,534 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

89a06142cf7a1d8c7f3b457cf828289dc3fcdcc46b0b9243f2f1d5b1d664d552

View on Chainz ↗

Height

#1,359,493

Difficulty

10.838528

Transactions

Size

20.73 KB

Version

Bits

0ad6a9c6

Nonce

740,637,696

Timestamp

12/7/2015, 3:24:55 PM

Confirmations

5,444,534

Mined by

⛏️ P2SHAN3f5z5UBkkwsNBkrzDkfaLBbkbkfDhYqY

Merkle Root

a4dbcf38113c999000e2c03161a972f47340bf53ebca3bed5644caa63b9394f7

Transactions (3)

Coinbase35b969e24a2544…0525518b97eda9

1 in → 1 out9.0500 XPM109 B

AN3f5z5U…bkfDhYqY

42ffcfb0b73363…e22c435a8cb0d8

22 in → 2 out501.2394 XPM3.26 KB

AJjnK9uC…VreFquR4 Ae4KgJZA…6LD1ukrC

57111213923102…3ad16b9f0d9c2c

119 in → 2 out470.0100 XPM17.28 KB

AdWadpp9…id5C3tgF AJaSKTps…JDpQDTzr

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.

6.762 × 10⁹³(94-digit number)

67623075590507497740…17000365248484212449

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

6.762 × 10⁹³(94-digit number)

67623075590507497740…17000365248484212449

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.762 × 10⁹³(94-digit number)

67623075590507497740…17000365248484212451

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

1.352 × 10⁹⁴(95-digit number)

13524615118101499548…34000730496968424899

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.352 × 10⁹⁴(95-digit number)

13524615118101499548…34000730496968424901

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

2.704 × 10⁹⁴(95-digit number)

27049230236202999096…68001460993936849799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.704 × 10⁹⁴(95-digit number)

27049230236202999096…68001460993936849801

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

5.409 × 10⁹⁴(95-digit number)

54098460472405998192…36002921987873699599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.409 × 10⁹⁴(95-digit number)

54098460472405998192…36002921987873699601

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

1.081 × 10⁹⁵(96-digit number)

10819692094481199638…72005843975747399199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.081 × 10⁹⁵(96-digit number)

10819692094481199638…72005843975747399201

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