Block #600,870

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/25/2014, 2:27:05 AM · Difficulty 10.9159 · 6,215,371 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
168f3062fdb1c82523f26d084ccf40bef6c26386d62189864bb07b4b2096c7bd

Height

#600,870

Difficulty

10.915937

Transactions

4

Size

1.01 KB

Version

2

Bits

0aea7ad1

Nonce

1,645,989,388

Timestamp

6/25/2014, 2:27:05 AM

Confirmations

6,215,371

Merkle Root

72b839ff9528e64ea84210137140a035b1a7c187cbedfc5b5c1518ffb9aa8ff2
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.

4.110 × 10⁹⁷(98-digit number)
41100613615564639484…93224696018343591841
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
4.110 × 10⁹⁷(98-digit number)
41100613615564639484…93224696018343591841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.220 × 10⁹⁷(98-digit number)
82201227231129278969…86449392036687183681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.644 × 10⁹⁸(99-digit number)
16440245446225855793…72898784073374367361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.288 × 10⁹⁸(99-digit number)
32880490892451711587…45797568146748734721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.576 × 10⁹⁸(99-digit number)
65760981784903423175…91595136293497469441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.315 × 10⁹⁹(100-digit number)
13152196356980684635…83190272586994938881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.630 × 10⁹⁹(100-digit number)
26304392713961369270…66380545173989877761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.260 × 10⁹⁹(100-digit number)
52608785427922738540…32761090347979755521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.052 × 10¹⁰⁰(101-digit number)
10521757085584547708…65522180695959511041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.104 × 10¹⁰⁰(101-digit number)
21043514171169095416…31044361391919022081
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:57,774,046 XPM·at block #6,816,240 · updates every 60s
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