Block #603,956

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/27/2014, 10:34:56 AM · Difficulty 10.9113 · 6,206,466 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
98fa64604d8f67533b1cc45b1e67ea15c5d2368cbca34270802a104e8b116e4f

Height

#603,956

Difficulty

10.911265

Transactions

1

Size

767 B

Version

2

Bits

0ae948a4

Nonce

421,680

Timestamp

6/27/2014, 10:34:56 AM

Confirmations

6,206,466

Merkle Root

3eafb7cc38caedad892e5f0c3c4b9ddccf2117cdb995959d6ebc6c03955876fd
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.

1.633 × 10⁹⁹(100-digit number)
16336528770387458344…30310792189464917281
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
1.633 × 10⁹⁹(100-digit number)
16336528770387458344…30310792189464917281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.267 × 10⁹⁹(100-digit number)
32673057540774916688…60621584378929834561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
6.534 × 10⁹⁹(100-digit number)
65346115081549833376…21243168757859669121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.306 × 10¹⁰⁰(101-digit number)
13069223016309966675…42486337515719338241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.613 × 10¹⁰⁰(101-digit number)
26138446032619933350…84972675031438676481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.227 × 10¹⁰⁰(101-digit number)
52276892065239866701…69945350062877352961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.045 × 10¹⁰¹(102-digit number)
10455378413047973340…39890700125754705921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.091 × 10¹⁰¹(102-digit number)
20910756826095946680…79781400251509411841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.182 × 10¹⁰¹(102-digit number)
41821513652191893361…59562800503018823681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
8.364 × 10¹⁰¹(102-digit number)
83643027304383786722…19125601006037647361
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:57,727,457 XPM·at block #6,810,421 · updates every 60s
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