Block #469,340

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/1/2014, 4:07:08 AM · Difficulty 10.4273 · 6,347,522 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cb1b5e668baf202cb38ae7891384020c54651807e18435010959cda658c59da3

Height

#469,340

Difficulty

10.427339

Transactions

8

Size

2.86 KB

Version

2

Bits

0a6d6618

Nonce

2,673

Timestamp

4/1/2014, 4:07:08 AM

Confirmations

6,347,522

Merkle Root

4cd866844cdd9cf02f89d66ab44a42d1a7b69765c8ac37560a1f3e1dfd8f61b4
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.

1.927 × 10⁹⁴(95-digit number)
19277245632119093349…16727270355212554241
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
1.927 × 10⁹⁴(95-digit number)
19277245632119093349…16727270355212554241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.855 × 10⁹⁴(95-digit number)
38554491264238186699…33454540710425108481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.710 × 10⁹⁴(95-digit number)
77108982528476373398…66909081420850216961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.542 × 10⁹⁵(96-digit number)
15421796505695274679…33818162841700433921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.084 × 10⁹⁵(96-digit number)
30843593011390549359…67636325683400867841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.168 × 10⁹⁵(96-digit number)
61687186022781098718…35272651366801735681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.233 × 10⁹⁶(97-digit number)
12337437204556219743…70545302733603471361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.467 × 10⁹⁶(97-digit number)
24674874409112439487…41090605467206942721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.934 × 10⁹⁶(97-digit number)
49349748818224878975…82181210934413885441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.869 × 10⁹⁶(97-digit number)
98699497636449757950…64362421868827770881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.973 × 10⁹⁷(98-digit number)
19739899527289951590…28724843737655541761
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 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
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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,778,940 XPM·at block #6,816,861 · updates every 60s
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