Block #1,376,208

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/19/2015, 8:41:02 PM · Difficulty 10.8084 · 5,450,552 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a61cfa50b1d735cff24a3def86a03bd045216d17b7bc7ed60974b4005abe9c8e

View on Chainz ↗

Height

#1,376,208

Difficulty

10.808376

Transactions

Size

1.86 KB

Version

Bits

0acef1bf

Nonce

1,710,122,934

Timestamp

12/19/2015, 8:41:02 PM

Confirmations

5,450,552

Mined by

⛏️ P2SHAWVjE8hRS97zTz5E94MjAvgHutPhoGbD84

Merkle Root

c901e32615acdf948307575944dc131f59bd016c798f704c66ceb9683314f475

Transactions (2)

Coinbase363a0758c16c9c…5a9dfbf985c967

1 in → 1 out8.6600 XPM109 B

AWVjE8hR…PhoGbD84

0a00e514c24574…af4037e83a04b3

11 in → 2 out447.7500 XPM1.67 KB

AHMTNugu…b1XfVhyA AQ6ABXxb…MUBBdSA9

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.

4.260 × 10⁹⁴(95-digit number)

42608233070949121537…60111853732637327359

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

4.260 × 10⁹⁴(95-digit number)

42608233070949121537…60111853732637327359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.260 × 10⁹⁴(95-digit number)

42608233070949121537…60111853732637327361

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

8.521 × 10⁹⁴(95-digit number)

85216466141898243074…20223707465274654719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.521 × 10⁹⁴(95-digit number)

85216466141898243074…20223707465274654721

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

1.704 × 10⁹⁵(96-digit number)

17043293228379648614…40447414930549309439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.704 × 10⁹⁵(96-digit number)

17043293228379648614…40447414930549309441

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

3.408 × 10⁹⁵(96-digit number)

34086586456759297229…80894829861098618879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.408 × 10⁹⁵(96-digit number)

34086586456759297229…80894829861098618881

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

6.817 × 10⁹⁵(96-digit number)

68173172913518594459…61789659722197237759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.817 × 10⁹⁵(96-digit number)

68173172913518594459…61789659722197237761

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 #1,376,208

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