Block #528,217

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/6/2014, 12:45:24 PM · Difficulty 10.8860 · 6,288,494 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
413dd5cd96beab32964a4e2f0dce5183b1ac8893f3d4afb0f2df4cf14d935933

Height

#528,217

Difficulty

10.886019

Transactions

4

Size

886 B

Version

2

Bits

0ae2d224

Nonce

60,103,080

Timestamp

5/6/2014, 12:45:24 PM

Confirmations

6,288,494

Merkle Root

3332eef0b208e89eb7b3fbe9e59a0a7f383083cc938215edd9f7b3e5427d8930
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.

4.066 × 10¹⁰⁰(101-digit number)
40660444874238181058…82479440247616983041
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
4.066 × 10¹⁰⁰(101-digit number)
40660444874238181058…82479440247616983041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.132 × 10¹⁰⁰(101-digit number)
81320889748476362116…64958880495233966081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.626 × 10¹⁰¹(102-digit number)
16264177949695272423…29917760990467932161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.252 × 10¹⁰¹(102-digit number)
32528355899390544846…59835521980935864321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.505 × 10¹⁰¹(102-digit number)
65056711798781089693…19671043961871728641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.301 × 10¹⁰²(103-digit number)
13011342359756217938…39342087923743457281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.602 × 10¹⁰²(103-digit number)
26022684719512435877…78684175847486914561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.204 × 10¹⁰²(103-digit number)
52045369439024871754…57368351694973829121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.040 × 10¹⁰³(104-digit number)
10409073887804974350…14736703389947658241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.081 × 10¹⁰³(104-digit number)
20818147775609948701…29473406779895316481
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:57,777,812 XPM·at block #6,816,710 · updates every 60s
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