Block #922,395

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 2/4/2015, 10:50:53 AM · Difficulty 10.9155 · 5,890,623 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
44aae0191d99cc166305d1781856ff6836104582d2b7d27e2130d8fdaf93a27c

Height

#922,395

Difficulty

10.915493

Transactions

5

Size

116.01 KB

Version

2

Bits

0aea5dc3

Nonce

87,295,434

Timestamp

2/4/2015, 10:50:53 AM

Confirmations

5,890,623

Merkle Root

260eb8ce0a962401e1a7b2046519e5ba6fbe8949e7213ab4c1ff420d9e9653c2
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out1094.7578 XPM28.96 KB
200 in → 1 out1005.8715 XPM28.95 KB
200 in → 1 out958.4099 XPM28.95 KB
200 in → 1 out1016.6840 XPM28.95 KB
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.

3.350 × 10⁹⁷(98-digit number)
33507875873314895578…04954623258562836479
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
3.350 × 10⁹⁷(98-digit number)
33507875873314895578…04954623258562836479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.701 × 10⁹⁷(98-digit number)
67015751746629791157…09909246517125672959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.340 × 10⁹⁸(99-digit number)
13403150349325958231…19818493034251345919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.680 × 10⁹⁸(99-digit number)
26806300698651916463…39636986068502691839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.361 × 10⁹⁸(99-digit number)
53612601397303832926…79273972137005383679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.072 × 10⁹⁹(100-digit number)
10722520279460766585…58547944274010767359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.144 × 10⁹⁹(100-digit number)
21445040558921533170…17095888548021534719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.289 × 10⁹⁹(100-digit number)
42890081117843066340…34191777096043069439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
8.578 × 10⁹⁹(100-digit number)
85780162235686132681…68383554192086138879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.715 × 10¹⁰⁰(101-digit number)
17156032447137226536…36767108384172277759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
3.431 × 10¹⁰⁰(101-digit number)
34312064894274453072…73534216768344555519
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:57,748,185 XPM·at block #6,813,017 · updates every 60s
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