Block #110,692

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/11/2013, 2:09:33 AM · Difficulty 9.6960 · 6,688,753 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c581ee309efc1e49c0433c674306541959c9fedff3ffba06cb72c64cea2faab6

Height

#110,692

Difficulty

9.695954

Transactions

2

Size

721 B

Version

2

Bits

09b22a05

Nonce

488,522

Timestamp

8/11/2013, 2:09:33 AM

Confirmations

6,688,753

Merkle Root

b04d1693e8c8ada998fc4815c6301b2d22674330068bcbec9ed223d98979b315
Transactions (2)
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.

1.086 × 10⁹⁸(99-digit number)
10863374842692086410…82614853715406378581
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
1.086 × 10⁹⁸(99-digit number)
10863374842692086410…82614853715406378581
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.172 × 10⁹⁸(99-digit number)
21726749685384172821…65229707430812757161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.345 × 10⁹⁸(99-digit number)
43453499370768345642…30459414861625514321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.690 × 10⁹⁸(99-digit number)
86906998741536691284…60918829723251028641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.738 × 10⁹⁹(100-digit number)
17381399748307338256…21837659446502057281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.476 × 10⁹⁹(100-digit number)
34762799496614676513…43675318893004114561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.952 × 10⁹⁹(100-digit number)
69525598993229353027…87350637786008229121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.390 × 10¹⁰⁰(101-digit number)
13905119798645870605…74701275572016458241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.781 × 10¹⁰⁰(101-digit number)
27810239597291741211…49402551144032916481
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,639,612 XPM·at block #6,799,444 · updates every 60s
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