Block #935,385

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 2/14/2015, 12:59:49 AM · Difficulty 10.9012 · 5,890,930 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0a58551f1f40c5b2fb5c5a59c2895cf264a6cbabdac6655eb22359bd6dbdda77

Height

#935,385

Difficulty

10.901154

Transactions

2

Size

603 B

Version

2

Bits

0ae6b205

Nonce

79,601,280

Timestamp

2/14/2015, 12:59:49 AM

Confirmations

5,890,930

Merkle Root

3154afd46c16a13ac8d0fd4f5c1d5a8af1b325fbb5f28ea965a3f0a852b65e22
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.

4.428 × 10⁹⁶(97-digit number)
44285695942236990902…05479507747712200959
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
4.428 × 10⁹⁶(97-digit number)
44285695942236990902…05479507747712200959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
8.857 × 10⁹⁶(97-digit number)
88571391884473981805…10959015495424401919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.771 × 10⁹⁷(98-digit number)
17714278376894796361…21918030990848803839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.542 × 10⁹⁷(98-digit number)
35428556753789592722…43836061981697607679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.085 × 10⁹⁷(98-digit number)
70857113507579185444…87672123963395215359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.417 × 10⁹⁸(99-digit number)
14171422701515837088…75344247926790430719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.834 × 10⁹⁸(99-digit number)
28342845403031674177…50688495853580861439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.668 × 10⁹⁸(99-digit number)
56685690806063348355…01376991707161722879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.133 × 10⁹⁹(100-digit number)
11337138161212669671…02753983414323445759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.267 × 10⁹⁹(100-digit number)
22674276322425339342…05507966828646891519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
4.534 × 10⁹⁹(100-digit number)
45348552644850678684…11015933657293783039
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:57,854,658 XPM·at block #6,826,314 · updates every 60s
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