Block #94,771

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/3/2013, 7:29:48 AM · Difficulty 9.2079 · 6,723,121 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
55b2993161e9eeb949ad401823103a56aef92a7bdf51ef0b24b05f347b49e590

Height

#94,771

Difficulty

9.207859

Transactions

3

Size

953 B

Version

2

Bits

09353637

Nonce

26,928

Timestamp

8/3/2013, 7:29:48 AM

Confirmations

6,723,121

Merkle Root

526a3963ca8d93e7e2d46917dcde41d00c3d341a308d820699d838a9d6848b1d
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.

6.197 × 10¹⁰⁷(108-digit number)
61979389049179678663…88252574486132929919
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.

1
origin − 1
6.197 × 10¹⁰⁷(108-digit number)
61979389049179678663…88252574486132929919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.239 × 10¹⁰⁸(109-digit number)
12395877809835935732…76505148972265859839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.479 × 10¹⁰⁸(109-digit number)
24791755619671871465…53010297944531719679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.958 × 10¹⁰⁸(109-digit number)
49583511239343742930…06020595889063439359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.916 × 10¹⁰⁸(109-digit number)
99167022478687485861…12041191778126878719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.983 × 10¹⁰⁹(110-digit number)
19833404495737497172…24082383556253757439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.966 × 10¹⁰⁹(110-digit number)
39666808991474994344…48164767112507514879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.933 × 10¹⁰⁹(110-digit number)
79333617982949988688…96329534225015029759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.586 × 10¹¹⁰(111-digit number)
15866723596589997737…92659068450030059519
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, …
Circulating Supply:57,787,197 XPM·at block #6,817,891 · updates every 60s
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