Block #69,844

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/20/2013, 10:41:53 AM · Difficulty 8.9915 · 6,722,926 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8f36e569f5e650ea9dfb4330f0eecd4db34ba895eaeb37b070f73f3c32eef4cd

View on Chainz ↗

Height

#69,844

Difficulty

8.991451

Transactions

Size

201 B

Version

Bits

08fdcfb9

Nonce

535

Timestamp

7/20/2013, 10:41:53 AM

Confirmations

6,722,926

Merkle Root

0ccd40990b635db3c40b2af513de2a58cd98edbd46d27c9d093ae4faab83efe0

Transactions (1)

Coinbase0ccd40990b635d…3ae4faab83efe0

1 in → 1 out12.3500 XPM110 B

AXSFye4r…ADf1YWCU

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.

3.887 × 10⁹⁶(97-digit number)

38872668129903114151…66898927790392850819

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

3.887 × 10⁹⁶(97-digit number)

38872668129903114151…66898927790392850819

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.887 × 10⁹⁶(97-digit number)

38872668129903114151…66898927790392850821

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

7.774 × 10⁹⁶(97-digit number)

77745336259806228303…33797855580785701639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.774 × 10⁹⁶(97-digit number)

77745336259806228303…33797855580785701641

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

1.554 × 10⁹⁷(98-digit number)

15549067251961245660…67595711161571403279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.554 × 10⁹⁷(98-digit number)

15549067251961245660…67595711161571403281

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

3.109 × 10⁹⁷(98-digit number)

31098134503922491321…35191422323142806559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.109 × 10⁹⁷(98-digit number)

31098134503922491321…35191422323142806561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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