Block #569,904

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/31/2014, 11:29:46 AM · Difficulty 10.9647 · 6,238,962 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
162bd1b4c5f7bb6176bb17af9902b0552dd2fe1070aff6f786154e60cea95f59

Height

#569,904

Difficulty

10.964703

Transactions

4

Size

999 B

Version

2

Bits

0af6f6cd

Nonce

8,943

Timestamp

5/31/2014, 11:29:46 AM

Confirmations

6,238,962

Merkle Root

7e03487b9473a5427985f23e7163ef07061c7425e86d8f71abc765cd11a68fbe
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.

3.029 × 10¹⁰¹(102-digit number)
30298911429507150208…10275200388694016001
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
3.029 × 10¹⁰¹(102-digit number)
30298911429507150208…10275200388694016001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.059 × 10¹⁰¹(102-digit number)
60597822859014300417…20550400777388032001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.211 × 10¹⁰²(103-digit number)
12119564571802860083…41100801554776064001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.423 × 10¹⁰²(103-digit number)
24239129143605720166…82201603109552128001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.847 × 10¹⁰²(103-digit number)
48478258287211440333…64403206219104256001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.695 × 10¹⁰²(103-digit number)
96956516574422880667…28806412438208512001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.939 × 10¹⁰³(104-digit number)
19391303314884576133…57612824876417024001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.878 × 10¹⁰³(104-digit number)
38782606629769152267…15225649752834048001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.756 × 10¹⁰³(104-digit number)
77565213259538304534…30451299505668096001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.551 × 10¹⁰⁴(105-digit number)
15513042651907660906…60902599011336192001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.102 × 10¹⁰⁴(105-digit number)
31026085303815321813…21805198022672384001
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:57,714,977 XPM·at block #6,808,865 · updates every 60s
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