Block #84,420

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/26/2013, 7:51:46 PM · Difficulty 9.2714 · 6,720,375 confirmations

2CC

Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header

Block Hash

49b31e5a423c66a5a4d32a4611581a61d05f14b5e171cb672a3c4971bf83f3cc

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Height

#84,420

Difficulty

9.271376

Transactions

Size

203 B

Version

Bits

094578e3

Nonce

64,087

Timestamp

7/26/2013, 7:51:46 PM

Confirmations

6,720,375

Mined by

⛏️ P2SHAcBadmkptMo3EwP8cg9ZUyqvJMGmhL921o

Merkle Root

f17ee273b450c2a04306e783712673b17a2d07d31ccf32ce1ab3ec5d5f956220

Transactions (1)

Coinbasef17ee273b450c2…b3ec5d5f956220

1 in → 1 out11.6200 XPM109 B

AcBadmkp…GmhL921o

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.

1.913 × 10¹⁰⁵(106-digit number)

19131795484969751937…11529219911291036091

Discovered Prime Numbers

p_k = 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.

origin + 1

1.913 × 10¹⁰⁵(106-digit number)

19131795484969751937…11529219911291036091

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.826 × 10¹⁰⁵(106-digit number)

38263590969939503875…23058439822582072181

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.652 × 10¹⁰⁵(106-digit number)

76527181939879007750…46116879645164144361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.530 × 10¹⁰⁶(107-digit number)

15305436387975801550…92233759290328288721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.061 × 10¹⁰⁶(107-digit number)

30610872775951603100…84467518580656577441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.122 × 10¹⁰⁶(107-digit number)

61221745551903206200…68935037161313154881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.224 × 10¹⁰⁷(108-digit number)

12244349110380641240…37870074322626309761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.448 × 10¹⁰⁷(108-digit number)

24488698220761282480…75740148645252619521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.897 × 10¹⁰⁷(108-digit number)

48977396441522564960…51480297290505239041

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 Cunningham Chain of the Second Kind. 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer