Block #134,990

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/26/2013, 9:05:16 AM · Difficulty 9.8075 · 6,657,041 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

22c8a10b4eddb86390f296a10f6339362ce5f0b9ec81f32d09065948bb908fa7

View on Chainz ↗

Height

#134,990

Difficulty

9.807546

Transactions

Size

202 B

Version

Bits

09cebb51

Nonce

9,491

Timestamp

8/26/2013, 9:05:16 AM

Confirmations

6,657,041

Merkle Root

63c2c0d0cdf386d9d482903a22e398bf03ce1b671a41b911e25883109f744367

Transactions (1)

Coinbase63c2c0d0cdf386…5883109f744367

1 in → 1 out10.3800 XPM109 B

AeBiUfRv…5nhNiU4o

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.

3.095 × 10¹⁰¹(102-digit number)

30958372155250502548…50210501639598911199

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

3.095 × 10¹⁰¹(102-digit number)

30958372155250502548…50210501639598911199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.095 × 10¹⁰¹(102-digit number)

30958372155250502548…50210501639598911201

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

6.191 × 10¹⁰¹(102-digit number)

61916744310501005096…00421003279197822399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.191 × 10¹⁰¹(102-digit number)

61916744310501005096…00421003279197822401

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

1.238 × 10¹⁰²(103-digit number)

12383348862100201019…00842006558395644799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.238 × 10¹⁰²(103-digit number)

12383348862100201019…00842006558395644801

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

2.476 × 10¹⁰²(103-digit number)

24766697724200402038…01684013116791289599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.476 × 10¹⁰²(103-digit number)

24766697724200402038…01684013116791289601

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

4.953 × 10¹⁰²(103-digit number)

49533395448400804077…03368026233582579199

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