Block #1,101,335

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 6/12/2015, 12:43:42 PM · Difficulty 10.7585 · 5,712,578 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b1decf5f65c7dfd0beed381aaa42da8e9efd4302aaa804bf542b51052a0ea3c5

Height

#1,101,335

Difficulty

10.758516

Transactions

3

Size

799 B

Version

2

Bits

0ac22e22

Nonce

433,383,030

Timestamp

6/12/2015, 12:43:42 PM

Confirmations

5,712,578

Merkle Root

31aa9a139ba901b163d57b4d2288cbbd322d03b0812b33bbbc76753de1e8cc67
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.

1.336 × 10⁹⁵(96-digit number)
13369572744883270929…18452997369993005439
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
1.336 × 10⁹⁵(96-digit number)
13369572744883270929…18452997369993005439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.673 × 10⁹⁵(96-digit number)
26739145489766541859…36905994739986010879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.347 × 10⁹⁵(96-digit number)
53478290979533083719…73811989479972021759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.069 × 10⁹⁶(97-digit number)
10695658195906616743…47623978959944043519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.139 × 10⁹⁶(97-digit number)
21391316391813233487…95247957919888087039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.278 × 10⁹⁶(97-digit number)
42782632783626466975…90495915839776174079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
8.556 × 10⁹⁶(97-digit number)
85565265567252933951…80991831679552348159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.711 × 10⁹⁷(98-digit number)
17113053113450586790…61983663359104696319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.422 × 10⁹⁷(98-digit number)
34226106226901173580…23967326718209392639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.845 × 10⁹⁷(98-digit number)
68452212453802347161…47934653436418785279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.369 × 10⁹⁸(99-digit number)
13690442490760469432…95869306872837570559
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:57,755,376 XPM·at block #6,813,912 · updates every 60s
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