Block #95,041

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/3/2013, 11:30:02 AM · Difficulty 9.2125 · 6,732,094 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
34420e8be99db2e6331986b1c3ecec815a2845099b3f4fe02392f2e63ecaac93

Height

#95,041

Difficulty

9.212490

Transactions

2

Size

1.32 KB

Version

2

Bits

093665bb

Nonce

1,993

Timestamp

8/3/2013, 11:30:02 AM

Confirmations

6,732,094

Merkle Root

c6c84d2ce32ee5516d18c4fafbcaba716a3c7b690560e98c693ce137a66fd70b
Transactions (2)
1 in → 1 out11.7900 XPM109 B
9 in → 1 out82.0000 XPM1.11 KB
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.

7.747 × 10¹²⁴(125-digit number)
77477071541901799417…11684937886017173019
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
7.747 × 10¹²⁴(125-digit number)
77477071541901799417…11684937886017173019
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.549 × 10¹²⁵(126-digit number)
15495414308380359883…23369875772034346039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.099 × 10¹²⁵(126-digit number)
30990828616760719766…46739751544068692079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.198 × 10¹²⁵(126-digit number)
61981657233521439533…93479503088137384159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.239 × 10¹²⁶(127-digit number)
12396331446704287906…86959006176274768319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.479 × 10¹²⁶(127-digit number)
24792662893408575813…73918012352549536639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.958 × 10¹²⁶(127-digit number)
49585325786817151627…47836024705099073279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.917 × 10¹²⁶(127-digit number)
99170651573634303254…95672049410198146559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.983 × 10¹²⁷(128-digit number)
19834130314726860650…91344098820396293119
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:57,861,260 XPM·at block #6,827,134 · updates every 60s
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