Block #567,276

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/29/2014, 3:08:10 PM · Difficulty 10.9649 · 6,249,118 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a9e38b477e630a6e65f9431f17ae42a4a2154a326987daed95e2e1f3eae2ef6a

Height

#567,276

Difficulty

10.964852

Transactions

1

Size

594 B

Version

2

Bits

0af70086

Nonce

259,229

Timestamp

5/29/2014, 3:08:10 PM

Confirmations

6,249,118

Merkle Root

20114a12b00beeda9bb5d6d8b4f95557c93bc57f26b658819816ef8978769f5a
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.

4.286 × 10⁹²(93-digit number)
42863361428077491447…49097550887507824641
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
4.286 × 10⁹²(93-digit number)
42863361428077491447…49097550887507824641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.572 × 10⁹²(93-digit number)
85726722856154982895…98195101775015649281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.714 × 10⁹³(94-digit number)
17145344571230996579…96390203550031298561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.429 × 10⁹³(94-digit number)
34290689142461993158…92780407100062597121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.858 × 10⁹³(94-digit number)
68581378284923986316…85560814200125194241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.371 × 10⁹⁴(95-digit number)
13716275656984797263…71121628400250388481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.743 × 10⁹⁴(95-digit number)
27432551313969594526…42243256800500776961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.486 × 10⁹⁴(95-digit number)
54865102627939189053…84486513601001553921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.097 × 10⁹⁵(96-digit number)
10973020525587837810…68973027202003107841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.194 × 10⁹⁵(96-digit number)
21946041051175675621…37946054404006215681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
4.389 × 10⁹⁵(96-digit number)
43892082102351351242…75892108808012431361
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:57,775,275 XPM·at block #6,816,393 · updates every 60s
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