Block #1,169,628

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 7/25/2015, 10:16:27 AM · Difficulty 10.9356 · 5,670,045 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2ffa6a1f36d5970262a9d985e43b68bf1e677c1cc9db8a9b32d6ae4b484dc3a1

Height

#1,169,628

Difficulty

10.935647

Transactions

2

Size

1.43 KB

Version

2

Bits

0aef8697

Nonce

882,847,891

Timestamp

7/25/2015, 10:16:27 AM

Confirmations

5,670,045

Merkle Root

bf4b6a3907d649dd950000c6cb54c062090e1f60ca098db5d03b24dde562b017
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.

3.704 × 10⁹³(94-digit number)
37043770183479887543…10287553383278273039
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
3.704 × 10⁹³(94-digit number)
37043770183479887543…10287553383278273039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.408 × 10⁹³(94-digit number)
74087540366959775087…20575106766556546079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.481 × 10⁹⁴(95-digit number)
14817508073391955017…41150213533113092159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.963 × 10⁹⁴(95-digit number)
29635016146783910035…82300427066226184319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.927 × 10⁹⁴(95-digit number)
59270032293567820070…64600854132452368639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.185 × 10⁹⁵(96-digit number)
11854006458713564014…29201708264904737279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.370 × 10⁹⁵(96-digit number)
23708012917427128028…58403416529809474559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.741 × 10⁹⁵(96-digit number)
47416025834854256056…16806833059618949119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.483 × 10⁹⁵(96-digit number)
94832051669708512112…33613666119237898239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.896 × 10⁹⁶(97-digit number)
18966410333941702422…67227332238475796479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
3.793 × 10⁹⁶(97-digit number)
37932820667883404844…34454664476951592959
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:57,961,673 XPM·at block #6,839,672 · updates every 60s
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