Block #242,188

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/3/2013, 3:09:54 PM · Difficulty 9.9592 · 6,568,703 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e9ee4620c53c19df957fda9d9c1d12d3549ebc45d2bbea0adaaf489277e32e76

View on Chainz ↗

Height

#242,188

Difficulty

9.959238

Transactions

Size

890 B

Version

Bits

09f590a2

Nonce

1,829

Timestamp

11/3/2013, 3:09:54 PM

Confirmations

6,568,703

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

6c75bc5f5be55b6e661b87457c34a782208a6bd3029f4671880d44aef4646325

Transactions (4)

Coinbasedb3542e489a169…88a46ed69a8a99

1 in → 2 out10.1000 XPM142 B

AKcbk49N…GJbKa7j1 AHsw4d6U…EnM8UXNZ

8badb780f60425…6285ee2790977c

1 in → 1 out10.1100 XPM158 B

ASNHbKyk…FYmTuopD

e28fcd14ff3bc3…3d35ff568070b8

1 in → 1 out10.1200 XPM157 B

Ad4tU5FR…YoLG8ved

fa1159b911f518…34bd39f893fc0f

2 in → 1 out133.1978 XPM340 B

AcUKPiDe…4rznYsnA

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.

9.616 × 10¹⁰¹(102-digit number)

96163307260499910628…43036281627361003519

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

9.616 × 10¹⁰¹(102-digit number)

96163307260499910628…43036281627361003519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.616 × 10¹⁰¹(102-digit number)

96163307260499910628…43036281627361003521

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

1.923 × 10¹⁰²(103-digit number)

19232661452099982125…86072563254722007039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.923 × 10¹⁰²(103-digit number)

19232661452099982125…86072563254722007041

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

3.846 × 10¹⁰²(103-digit number)

38465322904199964251…72145126509444014079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.846 × 10¹⁰²(103-digit number)

38465322904199964251…72145126509444014081

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

7.693 × 10¹⁰²(103-digit number)

76930645808399928502…44290253018888028159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.693 × 10¹⁰²(103-digit number)

76930645808399928502…44290253018888028161

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

1.538 × 10¹⁰³(104-digit number)

15386129161679985700…88580506037776056319

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

Block #242,188

Cookie Preferences