Block #242,794

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/3/2013, 10:27:25 PM · Difficulty 9.9606 · 6,559,720 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

718d7285e4d93d042a89f19cca76af8026bc806720deb773dae3bf5163bcbe49

View on Chainz ↗

Height

#242,794

Difficulty

9.960597

Transactions

Size

2.04 KB

Version

Bits

09f5e9b6

Nonce

15,432

Timestamp

11/3/2013, 10:27:25 PM

Confirmations

6,559,720

Mined by

⛏️ jRvAMypZdXSN9SRf28auDeE3guPFj5jJKu8wP

Merkle Root

e2f2c69972f7c95c652e00a42527a3a810d5cb5e91f0270e2a4d227a670f8356

Transactions (1)

Coinbasee2f2c69972f7c9…4d227a670f8356

1 in → 57 out10.0400 XPM1.95 KB

AMypZdXS…5jJKu8wP AeZmMFY8…mjAy5Mi4 AMsVa381…3WdZv7Jp AQtzUSwq…htAuF3yC AZWiC56x…NwextJca

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.

8.761 × 10¹⁰⁰(101-digit number)

87613637234765762228…71883208093601443839

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

8.761 × 10¹⁰⁰(101-digit number)

87613637234765762228…71883208093601443839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.761 × 10¹⁰⁰(101-digit number)

87613637234765762228…71883208093601443841

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

1.752 × 10¹⁰¹(102-digit number)

17522727446953152445…43766416187202887679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.752 × 10¹⁰¹(102-digit number)

17522727446953152445…43766416187202887681

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

3.504 × 10¹⁰¹(102-digit number)

35045454893906304891…87532832374405775359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.504 × 10¹⁰¹(102-digit number)

35045454893906304891…87532832374405775361

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

7.009 × 10¹⁰¹(102-digit number)

70090909787812609783…75065664748811550719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.009 × 10¹⁰¹(102-digit number)

70090909787812609783…75065664748811550721

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

1.401 × 10¹⁰²(103-digit number)

14018181957562521956…50131329497623101439

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