Block #87,925

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/29/2013, 6:12:26 AM · Difficulty 9.2722 · 6,715,977 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

4607b5a45568c7d20ba3558bc94f502f070ec4695476a5da4fa77042c329b141

View on Chainz ↗

Height

#87,925

Difficulty

9.272220

Transactions

Size

207 B

Version

Bits

0945b037

Nonce

13,618

Timestamp

7/29/2013, 6:12:26 AM

Confirmations

6,715,977

Mined by

⛏️ P2SHATe7tG7XMJeCcfKBVw1awGupC6yczDSDEp

Merkle Root

258160e87508be7373da08e0fe808280bf0dfd400a1116897109c045f5702e12

Transactions (1)

Coinbase258160e87508be…09c045f5702e12

1 in → 1 out11.6100 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.

5.157 × 10¹¹³(114-digit number)

51576457210388466592…84785260039684880301

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

5.157 × 10¹¹³(114-digit number)

51576457210388466592…84785260039684880301

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.031 × 10¹¹⁴(115-digit number)

10315291442077693318…69570520079369760601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.063 × 10¹¹⁴(115-digit number)

20630582884155386636…39141040158739521201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.126 × 10¹¹⁴(115-digit number)

41261165768310773273…78282080317479042401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

8.252 × 10¹¹⁴(115-digit number)

82522331536621546547…56564160634958084801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.650 × 10¹¹⁵(116-digit number)

16504466307324309309…13128321269916169601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.300 × 10¹¹⁵(116-digit number)

33008932614648618618…26256642539832339201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.601 × 10¹¹⁵(116-digit number)

66017865229297237237…52513285079664678401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.320 × 10¹¹⁶(117-digit number)

13203573045859447447…05026570159329356801

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