Block #87,429

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/28/2013, 9:32:25 PM · Difficulty 9.2757 · 6,703,563 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

9a46330865e1c85408459dc5e804dd7348dae75fc42a1433d3dc39788ed81bad

View on Chainz ↗

Height

#87,429

Difficulty

9.275650

Transactions

Size

205 B

Version

Bits

09469102

Nonce

46,562

Timestamp

7/28/2013, 9:32:25 PM

Confirmations

6,703,563

Merkle Root

59ea3becd097768efdadd0022c1afb32a946f3b300290ea1858a3401334ed352

Transactions (1)

Coinbase59ea3becd09776…8a3401334ed352

1 in → 1 out11.6100 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.

2.888 × 10¹⁰⁸(109-digit number)

28884717058030385588…09823473754228631559

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

2.888 × 10¹⁰⁸(109-digit number)

28884717058030385588…09823473754228631559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.776 × 10¹⁰⁸(109-digit number)

57769434116060771177…19646947508457263119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.155 × 10¹⁰⁹(110-digit number)

11553886823212154235…39293895016914526239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.310 × 10¹⁰⁹(110-digit number)

23107773646424308471…78587790033829052479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.621 × 10¹⁰⁹(110-digit number)

46215547292848616942…57175580067658104959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.243 × 10¹⁰⁹(110-digit number)

92431094585697233884…14351160135316209919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.848 × 10¹¹⁰(111-digit number)

18486218917139446776…28702320270632419839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.697 × 10¹¹⁰(111-digit number)

36972437834278893553…57404640541264839679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.394 × 10¹¹⁰(111-digit number)

73944875668557787107…14809281082529679359

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 First 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 1CC formula:

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

Cross-reference on Chainz Explorer