Block #946,013

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 2/21/2015, 12:51:22 PM · Difficulty 10.8986 · 5,871,839 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
96773aa1433ea58a423411e086d7b24f77a6e782e65a439b630bdd8f3ed88899

Height

#946,013

Difficulty

10.898594

Transactions

3

Size

2.09 KB

Version

2

Bits

0ae60a3a

Nonce

246,715,529

Timestamp

2/21/2015, 12:51:22 PM

Confirmations

5,871,839

Merkle Root

5faa63da74805c2883479b6bd083898b40970127de0266cb02c3a60eecbd528c
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.

1.529 × 10⁹⁷(98-digit number)
15299575507920114051…92643391814200348159
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
1.529 × 10⁹⁷(98-digit number)
15299575507920114051…92643391814200348159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.059 × 10⁹⁷(98-digit number)
30599151015840228103…85286783628400696319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.119 × 10⁹⁷(98-digit number)
61198302031680456207…70573567256801392639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.223 × 10⁹⁸(99-digit number)
12239660406336091241…41147134513602785279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.447 × 10⁹⁸(99-digit number)
24479320812672182482…82294269027205570559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.895 × 10⁹⁸(99-digit number)
48958641625344364965…64588538054411141119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
9.791 × 10⁹⁸(99-digit number)
97917283250688729931…29177076108822282239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.958 × 10⁹⁹(100-digit number)
19583456650137745986…58354152217644564479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.916 × 10⁹⁹(100-digit number)
39166913300275491972…16708304435289128959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.833 × 10⁹⁹(100-digit number)
78333826600550983945…33416608870578257919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.566 × 10¹⁰⁰(101-digit number)
15666765320110196789…66833217741156515839
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,786,882 XPM·at block #6,817,851 · updates every 60s
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