Block #1,320,990

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/10/2015, 9:24:26 AM · Difficulty 10.8593 · 5,493,269 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

37fbd1f59a65c89ae0441dfc7b4bc4fc042011902a48859a4e99acab45cc062a

View on Chainz ↗

Height

#1,320,990

Difficulty

10.859284

Transactions

Size

9.75 KB

Version

Bits

0adbfa0c

Nonce

1,142,235,702

Timestamp

11/10/2015, 9:24:26 AM

Confirmations

5,493,269

Mined by

⛏️ P2SHAaRQwSMRmMPtU6yVuWjL46w4YCctQin38i

Merkle Root

9daaebea5523e5b804d277522500fe9e578bc2d8812066c759a1712a02245a13

Transactions (3)

Coinbaseb56b272aa5e630…91d6fbf80d619e

1 in → 1 out8.5800 XPM110 B

AaRQwSMR…ctQin38i

ee834c5df9764a…62e988499e3e1e

22 in → 2 out112.4800 XPM3.25 KB

AcHCKe7w…HpDErLos AJPs3FuB…9Cxi7yrX

e325c00762f787…1f0f87ec0fc69b

43 in → 2 out87.8403 XPM6.30 KB

AQHE5e6H…xDwU3vYU AYfsqGgB…gwnmDghq

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.

6.300 × 10⁹⁷(98-digit number)

63000156159434006979…77918398223084421119

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

6.300 × 10⁹⁷(98-digit number)

63000156159434006979…77918398223084421119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.300 × 10⁹⁷(98-digit number)

63000156159434006979…77918398223084421121

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

1.260 × 10⁹⁸(99-digit number)

12600031231886801395…55836796446168842239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.260 × 10⁹⁸(99-digit number)

12600031231886801395…55836796446168842241

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

2.520 × 10⁹⁸(99-digit number)

25200062463773602791…11673592892337684479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.520 × 10⁹⁸(99-digit number)

25200062463773602791…11673592892337684481

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

5.040 × 10⁹⁸(99-digit number)

50400124927547205583…23347185784675368959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.040 × 10⁹⁸(99-digit number)

50400124927547205583…23347185784675368961

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

1.008 × 10⁹⁹(100-digit number)

10080024985509441116…46694371569350737919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.008 × 10⁹⁹(100-digit number)

10080024985509441116…46694371569350737921

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 #1,320,990

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