Block #1,447,804

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/8/2016, 10:05:00 AM · Difficulty 10.7595 · 5,366,442 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

830fe60d8f45e211f3e1664e161e4a53b66ac02d22a07187b22bdce853aa82b1

View on Chainz ↗

Height

#1,447,804

Difficulty

10.759480

Transactions

Size

698 B

Version

Bits

0ac26d50

Nonce

49,071,293

Timestamp

2/8/2016, 10:05:00 AM

Confirmations

5,366,442

Mined by

⛏️ P2SHAW6JomVivMKZweAwNnk86EPTxnRmV6WhbH

Merkle Root

bea6645e9cd3ae5eb6eef11ac9d91a7cbcd7bd35d0750830fe501dd61879057f

Transactions (2)

Coinbase23a55dc0e828b3…73a5e37a46c8ab

1 in → 1 out8.6300 XPM110 B

AW6JomVi…RmV6WhbH

6c6d3c8c347545…ea5fa7bb1ebf00

1 in → 10 out146.1670 XPM498 B

AcCoJQto…PuCYg79o AGk6f18N…wbHRjUVq ASXaymMq…xQTJu4rm AKPXjByo…VKXWyt83 ATmJibJc…64NvbM1L

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.

1.472 × 10⁹⁵(96-digit number)

14724277082332820978…34628623291912593499

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

1.472 × 10⁹⁵(96-digit number)

14724277082332820978…34628623291912593499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.472 × 10⁹⁵(96-digit number)

14724277082332820978…34628623291912593501

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

2.944 × 10⁹⁵(96-digit number)

29448554164665641956…69257246583825186999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.944 × 10⁹⁵(96-digit number)

29448554164665641956…69257246583825187001

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

5.889 × 10⁹⁵(96-digit number)

58897108329331283912…38514493167650373999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.889 × 10⁹⁵(96-digit number)

58897108329331283912…38514493167650374001

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

1.177 × 10⁹⁶(97-digit number)

11779421665866256782…77028986335300747999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.177 × 10⁹⁶(97-digit number)

11779421665866256782…77028986335300748001

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

2.355 × 10⁹⁶(97-digit number)

23558843331732513564…54057972670601495999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.355 × 10⁹⁶(97-digit number)

23558843331732513564…54057972670601496001

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 #1,447,804

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