Block #84,881

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/27/2013, 2:41:30 AM · Difficulty 9.2788 · 6,709,735 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

d9d5ee290b69710a45b865122831ba343956ddd4b03419a28079d2a1fbc85538

View on Chainz ↗

Height

#84,881

Difficulty

9.278810

Transactions

Size

201 B

Version

Bits

09476017

Nonce

74,299

Timestamp

7/27/2013, 2:41:30 AM

Confirmations

6,709,735

Mined by

⛏️ P2SHATe7tG7XMJeCcfKBVw1awGupC6yczDSDEp

Merkle Root

c6dff54c7bfa947017c230b30d5ddaebddaf4cad40a66cf1053438deb8599edc

Transactions (1)

Coinbasec6dff54c7bfa94…3438deb8599edc

1 in → 1 out11.6000 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.

9.641 × 10⁹⁹(100-digit number)

96417860965790870506…12810720978948929919

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

9.641 × 10⁹⁹(100-digit number)

96417860965790870506…12810720978948929919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.928 × 10¹⁰⁰(101-digit number)

19283572193158174101…25621441957897859839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.856 × 10¹⁰⁰(101-digit number)

38567144386316348202…51242883915795719679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.713 × 10¹⁰⁰(101-digit number)

77134288772632696405…02485767831591439359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.542 × 10¹⁰¹(102-digit number)

15426857754526539281…04971535663182878719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.085 × 10¹⁰¹(102-digit number)

30853715509053078562…09943071326365757439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.170 × 10¹⁰¹(102-digit number)

61707431018106157124…19886142652731514879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.234 × 10¹⁰²(103-digit number)

12341486203621231424…39772285305463029759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.468 × 10¹⁰²(103-digit number)

24682972407242462849…79544570610926059519

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