Block #86,603

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/28/2013, 6:12:23 AM · Difficulty 9.2891 · 6,708,827 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

f0a60bc09f38de6091a1e384dfd10e61367ee591018393eb05ce217d4370faa4

View on Chainz ↗

Height

#86,603

Difficulty

9.289138

Transactions

Size

201 B

Version

Bits

094a04f4

Nonce

191,620

Timestamp

7/28/2013, 6:12:23 AM

Confirmations

6,708,827

Mined by

⛏️ P2SHATe7tG7XMJeCcfKBVw1awGupC6yczDSDEp

Merkle Root

f21710982aad353f89aa324e2313b69d0312a8082c70c0c3679697dcba5be8b5

Transactions (1)

Coinbasef21710982aad35…9697dcba5be8b5

1 in → 1 out11.5700 XPM109 B

ATe7tG7X…yczDSDEp

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.

4.466 × 10⁹⁹(100-digit number)

44667943045536576877…53832369958324237501

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

4.466 × 10⁹⁹(100-digit number)

44667943045536576877…53832369958324237501

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

8.933 × 10⁹⁹(100-digit number)

89335886091073153755…07664739916648475001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.786 × 10¹⁰⁰(101-digit number)

17867177218214630751…15329479833296950001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.573 × 10¹⁰⁰(101-digit number)

35734354436429261502…30658959666593900001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

7.146 × 10¹⁰⁰(101-digit number)

71468708872858523004…61317919333187800001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.429 × 10¹⁰¹(102-digit number)

14293741774571704600…22635838666375600001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.858 × 10¹⁰¹(102-digit number)

28587483549143409201…45271677332751200001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.717 × 10¹⁰¹(102-digit number)

57174967098286818403…90543354665502400001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.143 × 10¹⁰²(103-digit number)

11434993419657363680…81086709331004800001

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