Block #569,475

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/31/2014, 4:26:01 AM · Difficulty 10.9646 · 6,240,100 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ec185782778d7c895a40a51555a15e8b32be4a4fb6461272027482e2f477df4e

Height

#569,475

Difficulty

10.964644

Transactions

2

Size

8.38 KB

Version

2

Bits

0af6f2e7

Nonce

809,134,115

Timestamp

5/31/2014, 4:26:01 AM

Confirmations

6,240,100

Merkle Root

cbcbedab98b605438bd77687d0bedaa8dc77f85c2ed02281f8497a63356f221d
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.

2.147 × 10⁹⁸(99-digit number)
21477244523754607080…24122763310214904321
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
2.147 × 10⁹⁸(99-digit number)
21477244523754607080…24122763310214904321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.295 × 10⁹⁸(99-digit number)
42954489047509214160…48245526620429808641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.590 × 10⁹⁸(99-digit number)
85908978095018428320…96491053240859617281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.718 × 10⁹⁹(100-digit number)
17181795619003685664…92982106481719234561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.436 × 10⁹⁹(100-digit number)
34363591238007371328…85964212963438469121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.872 × 10⁹⁹(100-digit number)
68727182476014742656…71928425926876938241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.374 × 10¹⁰⁰(101-digit number)
13745436495202948531…43856851853753876481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.749 × 10¹⁰⁰(101-digit number)
27490872990405897062…87713703707507752961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.498 × 10¹⁰⁰(101-digit number)
54981745980811794125…75427407415015505921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.099 × 10¹⁰¹(102-digit number)
10996349196162358825…50854814830031011841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.199 × 10¹⁰¹(102-digit number)
21992698392324717650…01709629660062023681
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:57,720,677 XPM·at block #6,809,574 · updates every 60s
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