Block #2,168,452

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/20/2017, 7:01:42 AM · Difficulty 10.8982 · 4,646,401 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
169449a9da0b20bd27fa2c72bd478149f10a6791f9b6bbad9dc900abb1653ce2

Height

#2,168,452

Difficulty

10.898192

Transactions

2

Size

2.87 KB

Version

2

Bits

0ae5efe4

Nonce

899,485,276

Timestamp

6/20/2017, 7:01:42 AM

Confirmations

4,646,401

Merkle Root

9cc04648ac48b521024cf011b0c459ace3a356fd792d86c42a7b0b961bf9b4c4
Transactions (2)
1 in → 1 out8.5000 XPM109 B
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.

7.810 × 10⁹³(94-digit number)
78100758686283511828…05450702796370048871
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
7.810 × 10⁹³(94-digit number)
78100758686283511828…05450702796370048871
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.562 × 10⁹⁴(95-digit number)
15620151737256702365…10901405592740097741
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.124 × 10⁹⁴(95-digit number)
31240303474513404731…21802811185480195481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.248 × 10⁹⁴(95-digit number)
62480606949026809462…43605622370960390961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.249 × 10⁹⁵(96-digit number)
12496121389805361892…87211244741920781921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.499 × 10⁹⁵(96-digit number)
24992242779610723785…74422489483841563841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.998 × 10⁹⁵(96-digit number)
49984485559221447570…48844978967683127681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.996 × 10⁹⁵(96-digit number)
99968971118442895140…97689957935366255361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.999 × 10⁹⁶(97-digit number)
19993794223688579028…95379915870732510721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.998 × 10⁹⁶(97-digit number)
39987588447377158056…90759831741465021441
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:57,762,907 XPM·at block #6,814,852 · updates every 60s
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