Block #1,201,718

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 8/20/2015, 1:14:19 PM · Difficulty 10.8094 · 5,625,243 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
44867203e32e7eb593c7be4e4de977864a0de9d48c33411a84703e1ceffedf51

Height

#1,201,718

Difficulty

10.809394

Transactions

2

Size

574 B

Version

2

Bits

0acf346a

Nonce

115,280

Timestamp

8/20/2015, 1:14:19 PM

Confirmations

5,625,243

Merkle Root

5c0992d91e9e62b657578fbaf7fb485b1c0ca8e3d740e1f63df8f94752ee4e33
Transactions (2)
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.

1.638 × 10⁹⁷(98-digit number)
16380127832565804306…56273576578621233519
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
1.638 × 10⁹⁷(98-digit number)
16380127832565804306…56273576578621233519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.276 × 10⁹⁷(98-digit number)
32760255665131608612…12547153157242467039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.552 × 10⁹⁷(98-digit number)
65520511330263217225…25094306314484934079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.310 × 10⁹⁸(99-digit number)
13104102266052643445…50188612628969868159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.620 × 10⁹⁸(99-digit number)
26208204532105286890…00377225257939736319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.241 × 10⁹⁸(99-digit number)
52416409064210573780…00754450515879472639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.048 × 10⁹⁹(100-digit number)
10483281812842114756…01508901031758945279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.096 × 10⁹⁹(100-digit number)
20966563625684229512…03017802063517890559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.193 × 10⁹⁹(100-digit number)
41933127251368459024…06035604127035781119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
8.386 × 10⁹⁹(100-digit number)
83866254502736918048…12071208254071562239
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,859,864 XPM·at block #6,826,960 · updates every 60s
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