Block #155,334

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/8/2013, 6:31:26 AM · Difficulty 9.8656 · 6,637,444 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8c882fb5fe952c51e67d3f94ca4db20bbc47471f3c0bdec8432f289af071f5fd

View on Chainz ↗

Height

#155,334

Difficulty

9.865623

Transactions

Size

197 B

Version

Bits

09dd9977

Nonce

911,631

Timestamp

9/8/2013, 6:31:26 AM

Confirmations

6,637,444

Merkle Root

9d52c97bddac4666c64f8a5c22b2488cd25dc8d68899069c6f904d468ed876f0

Transactions (1)

Coinbase9d52c97bddac46…904d468ed876f0

1 in → 1 out10.2600 XPM109 B

AJQ7bqzh…oY2ANRaW

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.

3.902 × 10⁹⁰(91-digit number)

39022842051624272427…12787237641970703999

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

3.902 × 10⁹⁰(91-digit number)

39022842051624272427…12787237641970703999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.902 × 10⁹⁰(91-digit number)

39022842051624272427…12787237641970704001

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

7.804 × 10⁹⁰(91-digit number)

78045684103248544854…25574475283941407999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.804 × 10⁹⁰(91-digit number)

78045684103248544854…25574475283941408001

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

1.560 × 10⁹¹(92-digit number)

15609136820649708970…51148950567882815999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.560 × 10⁹¹(92-digit number)

15609136820649708970…51148950567882816001

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

3.121 × 10⁹¹(92-digit number)

31218273641299417941…02297901135765631999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.121 × 10⁹¹(92-digit number)

31218273641299417941…02297901135765632001

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

6.243 × 10⁹¹(92-digit number)

62436547282598835883…04595802271531263999

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