Block #1,520,651

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/31/2016, 9:27:09 PM · Difficulty 10.5914 · 5,289,286 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cab7a497805441796ca1ad36767c0e23eeb99b771d21dd9c8aaee64b368aa863

View on Chainz ↗

Height

#1,520,651

Difficulty

10.591384

Transactions

Size

13.42 KB

Version

Bits

0a9764f5

Nonce

106,427,345

Timestamp

3/31/2016, 9:27:09 PM

Confirmations

5,289,286

Mined by

⛏️ P2SHATTvc3FCxW3JpEWXYwXCKj5jDiwdkoAM1V

Merkle Root

d1019a059c868587c8eeaec1dc83ca2324d7117d9bd8452e75b2ede4cf28d4b1

Transactions (2)

Coinbase4c016be755ebd3…dc2c39d32f7e98

1 in → 1 out9.0500 XPM109 B

ATTvc3FC…wdkoAM1V

d7567e51164628…a28ac86254007b

91 in → 2 out503.7315 XPM13.23 KB

AGkURQ5X…xvK8ptoh AWtZ86fs…tCejsY8G

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.

2.127 × 10⁹¹(92-digit number)

21273859779879409920…23684450473406850079

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

2.127 × 10⁹¹(92-digit number)

21273859779879409920…23684450473406850079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.127 × 10⁹¹(92-digit number)

21273859779879409920…23684450473406850081

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

4.254 × 10⁹¹(92-digit number)

42547719559758819840…47368900946813700159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.254 × 10⁹¹(92-digit number)

42547719559758819840…47368900946813700161

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

8.509 × 10⁹¹(92-digit number)

85095439119517639681…94737801893627400319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.509 × 10⁹¹(92-digit number)

85095439119517639681…94737801893627400321

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

1.701 × 10⁹²(93-digit number)

17019087823903527936…89475603787254800639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.701 × 10⁹²(93-digit number)

17019087823903527936…89475603787254800641

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

3.403 × 10⁹²(93-digit number)

34038175647807055872…78951207574509601279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.403 × 10⁹²(93-digit number)

34038175647807055872…78951207574509601281

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 #1,520,651

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