Block #169,336

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/17/2013, 10:32:34 PM · Difficulty 9.8683 · 6,622,651 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7669a807c8957ea8986c72fb4a7d8ef16757e31ed504c54a5d76ca269690c01c

View on Chainz ↗

Height

#169,336

Difficulty

9.868300

Transactions

Size

571 B

Version

Bits

09de48e4

Nonce

166,867

Timestamp

9/17/2013, 10:32:34 PM

Confirmations

6,622,651

Merkle Root

502e7496e86a1db695c4922b617b8447bae2687ae9d35f50cb9a5244cf4ba1b2

Transactions (2)

Coinbase88110c2f174847…243b579a1eac30

1 in → 1 out10.2600 XPM109 B

ALuMmhF7…cAn1cCmG

bb9853fcae7ed1…27c74a325dae0a

2 in → 2 out13.4732 XPM372 B

AcobKUjM…RiiNdfve ALpthvGg…D1g5z4CT

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.

2.043 × 10⁹⁴(95-digit number)

20435611490606917460…17655729049269570719

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

2.043 × 10⁹⁴(95-digit number)

20435611490606917460…17655729049269570719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.043 × 10⁹⁴(95-digit number)

20435611490606917460…17655729049269570721

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

4.087 × 10⁹⁴(95-digit number)

40871222981213834921…35311458098539141439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.087 × 10⁹⁴(95-digit number)

40871222981213834921…35311458098539141441

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

8.174 × 10⁹⁴(95-digit number)

81742445962427669843…70622916197078282879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.174 × 10⁹⁴(95-digit number)

81742445962427669843…70622916197078282881

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

1.634 × 10⁹⁵(96-digit number)

16348489192485533968…41245832394156565759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.634 × 10⁹⁵(96-digit number)

16348489192485533968…41245832394156565761

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

3.269 × 10⁹⁵(96-digit number)

32696978384971067937…82491664788313131519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.269 × 10⁹⁵(96-digit number)

32696978384971067937…82491664788313131521

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