Block #1,448,332

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/8/2016, 7:03:43 PM · Difficulty 10.7590 · 5,389,295 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

753f6b99854f1bae5ac6d04c190ed0219d241e01d37be83cd75a77f03d1294bd

View on Chainz ↗

Height

#1,448,332

Difficulty

10.758962

Transactions

Size

1.01 KB

Version

Bits

0ac24b55

Nonce

970,939,552

Timestamp

2/8/2016, 7:03:43 PM

Confirmations

5,389,295

Mined by

⛏️ P2SHAU5ZPJXk9kb8PkB28Gz3YtMRBLYLHQiYMT

Merkle Root

d663d3b5e55206f325d67b04e01cbe584ba7982260627fa719105d6c1ffc59d4

Transactions (2)

Coinbase565b0087bfb207…3fe2142ae01683

1 in → 1 out8.6400 XPM109 B

AU5ZPJXk…YLHQiYMT

77e068879eaef5…8929a3f33fb6a3

1 in → 20 out138.8115 XPM837 B

AZnZSZYR…CtuVHQwx Ac6ZACeG…x2mgUBAL ASG21nzq…iMYaGLq3 AXWJqtt6…gihu42Qs AZ2Dv6vs…YoKVyFme

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.

3.302 × 10⁹⁴(95-digit number)

33025227774897832379…65493033762713089759

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

3.302 × 10⁹⁴(95-digit number)

33025227774897832379…65493033762713089759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.302 × 10⁹⁴(95-digit number)

33025227774897832379…65493033762713089761

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

6.605 × 10⁹⁴(95-digit number)

66050455549795664759…30986067525426179519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.605 × 10⁹⁴(95-digit number)

66050455549795664759…30986067525426179521

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

1.321 × 10⁹⁵(96-digit number)

13210091109959132951…61972135050852359039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.321 × 10⁹⁵(96-digit number)

13210091109959132951…61972135050852359041

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

2.642 × 10⁹⁵(96-digit number)

26420182219918265903…23944270101704718079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.642 × 10⁹⁵(96-digit number)

26420182219918265903…23944270101704718081

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

5.284 × 10⁹⁵(96-digit number)

52840364439836531807…47888540203409436159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.284 × 10⁹⁵(96-digit number)

52840364439836531807…47888540203409436161

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 #1,448,332

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