Block #155,660

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/8/2013, 11:42:09 AM · Difficulty 9.8659 · 6,636,464 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ced46bac709691e035c15c3d70ac0dab6b244fd6a0a2ca0ffa4bcc8f8ee823b0

View on Chainz ↗

Height

#155,660

Difficulty

9.865920

Transactions

Size

1.43 KB

Version

Bits

09ddacf2

Nonce

9,873

Timestamp

9/8/2013, 11:42:09 AM

Confirmations

6,636,464

Merkle Root

d2a7870bc5a33d8d0f7b8c9f2bba8c8fa884536de47d311b7c4a82d8c51b9473

Transactions (4)

Coinbase53ca55d0f64337…2381dcd979d477

1 in → 1 out10.2900 XPM109 B

AGDy6Ak4…W5DYTbMC

9f97a8aff06dfd…596cc81050c13c

1 in → 2 out8.2261 XPM226 B

ARgqfD4F…eXoyzyof APEJY25v…z1QVp8xN

a70103a51d6ddb…f9bb27149574b9

5 in → 2 out10.1006 XPM818 B

AGNGCXYN…J29kEHwu ALp4QBZx…yAnNHja9

223f1c1957fe52…5f64a5db1b555a

1 in → 2 out4.8736 XPM225 B

APETbh8q…tueyUWi5 ANShBaCx…NttHiwPk

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.

2.746 × 10⁹¹(92-digit number)

27467387919239925031…09741690757473141029

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

2.746 × 10⁹¹(92-digit number)

27467387919239925031…09741690757473141029

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.746 × 10⁹¹(92-digit number)

27467387919239925031…09741690757473141031

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

5.493 × 10⁹¹(92-digit number)

54934775838479850063…19483381514946282059

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.493 × 10⁹¹(92-digit number)

54934775838479850063…19483381514946282061

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

1.098 × 10⁹²(93-digit number)

10986955167695970012…38966763029892564119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.098 × 10⁹²(93-digit number)

10986955167695970012…38966763029892564121

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

2.197 × 10⁹²(93-digit number)

21973910335391940025…77933526059785128239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.197 × 10⁹²(93-digit number)

21973910335391940025…77933526059785128241

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

4.394 × 10⁹²(93-digit number)

43947820670783880050…55867052119570256479

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