Block #1,270,169

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/7/2015, 12:06:38 AM · Difficulty 10.8157 · 5,557,018 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

26610c937e2d856c2673dd756d9a870039f93c95c7e7706acee11b78467fa81a

View on Chainz ↗

Height

#1,270,169

Difficulty

10.815744

Transactions

Size

1.22 KB

Version

Bits

0ad0d49e

Nonce

815,819,497

Timestamp

10/7/2015, 12:06:38 AM

Confirmations

5,557,018

Mined by

⛏️ P2SHAWGF7Zq8XC64thKE4NWkJdgDcuXkqHqUug

Merkle Root

b636876b6842b51b5901c91e624647c697d9b45b737944b5078c13948070ae6e

Transactions (4)

Coinbase620e64dda90ade…d4115924853633

1 in → 1 out8.5600 XPM109 B

AWGF7Zq8…XkqHqUug

599dc9cfeed179…930de4e354e6fb

1 in → 13 out48.5051 XPM600 B

ATyHFdjS…kku74cEm AX6oJXsR…NsFeV4Bn Ad6hP4a6…X8i78oH2 AVumhxGR…b68JCZo4 AWhHG3cs…Qkg16jh4

5b5b34f026d988…c290c698b50d85

1 in → 2 out5.8975 XPM225 B

AJ2iepBy…MkQ8x7fw APaYVt8e…rPF99zd2

5aeed0dfcdd8ad…f739a471c11c22

1 in → 2 out3.3935 XPM225 B

AHT3AxLA…wyZzw8fz AXrTw46X…e1dGvSFf

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.

3.051 × 10⁹³(94-digit number)

30518673052052240871…22993752060220153619

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

3.051 × 10⁹³(94-digit number)

30518673052052240871…22993752060220153619

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.051 × 10⁹³(94-digit number)

30518673052052240871…22993752060220153621

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

6.103 × 10⁹³(94-digit number)

61037346104104481742…45987504120440307239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.103 × 10⁹³(94-digit number)

61037346104104481742…45987504120440307241

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

1.220 × 10⁹⁴(95-digit number)

12207469220820896348…91975008240880614479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.220 × 10⁹⁴(95-digit number)

12207469220820896348…91975008240880614481

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

2.441 × 10⁹⁴(95-digit number)

24414938441641792696…83950016481761228959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.441 × 10⁹⁴(95-digit number)

24414938441641792696…83950016481761228961

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

4.882 × 10⁹⁴(95-digit number)

48829876883283585393…67900032963522457919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.882 × 10⁹⁴(95-digit number)

48829876883283585393…67900032963522457921

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 #1,270,169

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