Block #162,536

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/13/2013, 9:17:38 AM · Difficulty 9.8614 · 6,628,619 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

190e38702fcc0028884c5b0a63df1d2a340903cf0f760af94fcda0c91f9a3d4c

View on Chainz ↗

Height

#162,536

Difficulty

9.861371

Transactions

Size

199 B

Version

Bits

09dc82cb

Nonce

294,137

Timestamp

9/13/2013, 9:17:38 AM

Confirmations

6,628,619

Merkle Root

12e1dfc845e535215792fe6ef33f274a97a418824216f7f9e891df96bb16b3fd

Transactions (1)

Coinbase12e1dfc845e535…91df96bb16b3fd

1 in → 1 out10.2700 XPM109 B

AKnjzMcH…jxdaXcap

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.

2.727 × 10⁹⁴(95-digit number)

27277079922053116313…90323288386383312399

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

2.727 × 10⁹⁴(95-digit number)

27277079922053116313…90323288386383312399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.727 × 10⁹⁴(95-digit number)

27277079922053116313…90323288386383312401

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

5.455 × 10⁹⁴(95-digit number)

54554159844106232626…80646576772766624799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.455 × 10⁹⁴(95-digit number)

54554159844106232626…80646576772766624801

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

1.091 × 10⁹⁵(96-digit number)

10910831968821246525…61293153545533249599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.091 × 10⁹⁵(96-digit number)

10910831968821246525…61293153545533249601

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

2.182 × 10⁹⁵(96-digit number)

21821663937642493050…22586307091066499199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.182 × 10⁹⁵(96-digit number)

21821663937642493050…22586307091066499201

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

4.364 × 10⁹⁵(96-digit number)

43643327875284986101…45172614182132998399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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