Block #90,363

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/31/2013, 1:39:17 AM · Difficulty 9.2475 · 6,699,476 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

3c032ab85f7738038719a270b668a171be8e889b92e093ade936a9735527cec9

View on Chainz ↗

Height

#90,363

Difficulty

9.247532

Transactions

Size

204 B

Version

Bits

093f5e41

Nonce

74,401

Timestamp

7/31/2013, 1:39:17 AM

Confirmations

6,699,476

Merkle Root

c7dbe5cbe1f0dc51ed68edbd1f6aa01ecfbcf64ab861c815b2285e8fa379440f

Transactions (1)

Coinbasec7dbe5cbe1f0dc…285e8fa379440f

1 in → 1 out11.6800 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.

2.429 × 10¹⁰⁷(108-digit number)

24297052286722815869…96996887332316737919

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

2.429 × 10¹⁰⁷(108-digit number)

24297052286722815869…96996887332316737919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.859 × 10¹⁰⁷(108-digit number)

48594104573445631739…93993774664633475839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.718 × 10¹⁰⁷(108-digit number)

97188209146891263479…87987549329266951679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.943 × 10¹⁰⁸(109-digit number)

19437641829378252695…75975098658533903359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.887 × 10¹⁰⁸(109-digit number)

38875283658756505391…51950197317067806719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.775 × 10¹⁰⁸(109-digit number)

77750567317513010783…03900394634135613439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.555 × 10¹⁰⁹(110-digit number)

15550113463502602156…07800789268271226879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.110 × 10¹⁰⁹(110-digit number)

31100226927005204313…15601578536542453759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.220 × 10¹⁰⁹(110-digit number)

62200453854010408627…31203157073084907519

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