Block #1,103,746

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 6/14/2015, 4:03:29 AM · Difficulty 10.7609 · 5,713,795 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9710978a4b7fc44b7155f4d98c9ebfbad8bdd2097244c051ec4d1a40ce612640

Height

#1,103,746

Difficulty

10.760910

Transactions

3

Size

1.36 KB

Version

2

Bits

0ac2cb02

Nonce

1,061,970,083

Timestamp

6/14/2015, 4:03:29 AM

Confirmations

5,713,795

Merkle Root

4284e0d5e855ea78c2ea7eab79eb0a9067ad23662545c8b76a84eecc3e7b97b7
Transactions (3)
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.

8.765 × 10⁹³(94-digit number)
87650658968770664716…43898558087283036339
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
8.765 × 10⁹³(94-digit number)
87650658968770664716…43898558087283036339
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.753 × 10⁹⁴(95-digit number)
17530131793754132943…87797116174566072679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.506 × 10⁹⁴(95-digit number)
35060263587508265886…75594232349132145359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.012 × 10⁹⁴(95-digit number)
70120527175016531773…51188464698264290719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.402 × 10⁹⁵(96-digit number)
14024105435003306354…02376929396528581439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.804 × 10⁹⁵(96-digit number)
28048210870006612709…04753858793057162879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.609 × 10⁹⁵(96-digit number)
56096421740013225418…09507717586114325759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.121 × 10⁹⁶(97-digit number)
11219284348002645083…19015435172228651519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.243 × 10⁹⁶(97-digit number)
22438568696005290167…38030870344457303039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.487 × 10⁹⁶(97-digit number)
44877137392010580334…76061740688914606079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
8.975 × 10⁹⁶(97-digit number)
89754274784021160669…52123481377829212159
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:57,784,380 XPM·at block #6,817,540 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy Policy·

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

·Privacy Policy