Block #82,146

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/25/2013, 5:34:49 AM · Difficulty 9.2747 · 6,714,139 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0bddd12d1a541cef0c588be4af827296230342b6fd7c1f99b0ed25ba3463f689

View on Chainz ↗

Height

#82,146

Difficulty

9.274739

Transactions

Size

1018 B

Version

Bits

09465544

Nonce

204,968

Timestamp

7/25/2013, 5:34:49 AM

Confirmations

6,714,139

Mined by

⛏️ P2SHAaFhxEw7541WJT7NQGLAa9HF3cdYkZJvKJ

Merkle Root

a0cf4d26abb2a73e119d52b0042fa166f73188487769e9162149abb2c05957ca

Transactions (2)

Coinbase9a7f38750b2065…fe13ff1cb454c1

1 in → 1 out11.6200 XPM109 B

AaFhxEw7…dYkZJvKJ

483a3bca3e9e9b…6312e381b268f3

5 in → 2 out14241.5804 XPM815 B

AHUHdR12…b1vdLXJM ANwTcopq…mbdiwg2P

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.

2.282 × 10¹⁰³(104-digit number)

22823499695486788569…29053800344604083609

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

2.282 × 10¹⁰³(104-digit number)

22823499695486788569…29053800344604083609

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.282 × 10¹⁰³(104-digit number)

22823499695486788569…29053800344604083611

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

4.564 × 10¹⁰³(104-digit number)

45646999390973577139…58107600689208167219

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.564 × 10¹⁰³(104-digit number)

45646999390973577139…58107600689208167221

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

9.129 × 10¹⁰³(104-digit number)

91293998781947154278…16215201378416334439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.129 × 10¹⁰³(104-digit number)

91293998781947154278…16215201378416334441

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

1.825 × 10¹⁰⁴(105-digit number)

18258799756389430855…32430402756832668879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.825 × 10¹⁰⁴(105-digit number)

18258799756389430855…32430402756832668881

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

3.651 × 10¹⁰⁴(105-digit number)

36517599512778861711…64860805513665337759

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