Block #1,336,171

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/21/2015, 10:12:47 PM · Difficulty 10.8138 · 5,480,608 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fda16ef7b7f9e3933693340192986ed3e25d02e58edccc49ff9b8318f954aeaa

Height

#1,336,171

Difficulty

10.813800

Transactions

2

Size

575 B

Version

2

Bits

0ad0552d

Nonce

43,350,233

Timestamp

11/21/2015, 10:12:47 PM

Confirmations

5,480,608

Merkle Root

d6615792ca1d9ca23f30ad9702ee63f7755b7d8d1f36b5838878d76420ba4ee5
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.

5.231 × 10⁹⁴(95-digit number)
52313623870911713069…06019776040881107679
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
5.231 × 10⁹⁴(95-digit number)
52313623870911713069…06019776040881107679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.046 × 10⁹⁵(96-digit number)
10462724774182342613…12039552081762215359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.092 × 10⁹⁵(96-digit number)
20925449548364685227…24079104163524430719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.185 × 10⁹⁵(96-digit number)
41850899096729370455…48158208327048861439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
8.370 × 10⁹⁵(96-digit number)
83701798193458740910…96316416654097722879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.674 × 10⁹⁶(97-digit number)
16740359638691748182…92632833308195445759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.348 × 10⁹⁶(97-digit number)
33480719277383496364…85265666616390891519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.696 × 10⁹⁶(97-digit number)
66961438554766992728…70531333232781783039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.339 × 10⁹⁷(98-digit number)
13392287710953398545…41062666465563566079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.678 × 10⁹⁷(98-digit number)
26784575421906797091…82125332931127132159
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:57,778,267 XPM·at block #6,816,778 · updates every 60s
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