Block #922,253

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/4/2015, 7:54:03 AM · Difficulty 10.9161 · 5,874,269 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2cf8511f835f745f1d1ee74e1c2657e9b4fc30f47afc20fc1c5cb4c6f4bbf4c3

Height

#922,253

Difficulty

10.916069

Transactions

4

Size

87.10 KB

Version

2

Bits

0aea8381

Nonce

2,019,466,694

Timestamp

2/4/2015, 7:54:03 AM

Confirmations

5,874,269

Merkle Root

17cf8176e779f5cdba8908c16e4f3d82ec2c81dacbd0fdcb933392981940fe81
Transactions (4)
1 in → 1 out9.2800 XPM116 B
200 in → 1 out1157.8370 XPM28.96 KB
200 in → 1 out998.1816 XPM28.96 KB
200 in → 1 out1042.4350 XPM28.97 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.

3.488 × 10⁹⁷(98-digit number)
34882381789481844420…75229636553741113601
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
3.488 × 10⁹⁷(98-digit number)
34882381789481844420…75229636553741113601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.976 × 10⁹⁷(98-digit number)
69764763578963688840…50459273107482227201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.395 × 10⁹⁸(99-digit number)
13952952715792737768…00918546214964454401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.790 × 10⁹⁸(99-digit number)
27905905431585475536…01837092429928908801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.581 × 10⁹⁸(99-digit number)
55811810863170951072…03674184859857817601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.116 × 10⁹⁹(100-digit number)
11162362172634190214…07348369719715635201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.232 × 10⁹⁹(100-digit number)
22324724345268380429…14696739439431270401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.464 × 10⁹⁹(100-digit number)
44649448690536760858…29393478878862540801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.929 × 10⁹⁹(100-digit number)
89298897381073521716…58786957757725081601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.785 × 10¹⁰⁰(101-digit number)
17859779476214704343…17573915515450163201
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,616,173 XPM·at block #6,796,521 · 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.