Block #492,490

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/15/2014, 4:19:14 AM · Difficulty 10.6880 · 6,313,360 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
50beb9cebf4332bef6d717adb2f672c34b0cba469c1615a1e96ec6f458ec6c43

Height

#492,490

Difficulty

10.688025

Transactions

4

Size

886 B

Version

2

Bits

0ab02265

Nonce

516,129,851

Timestamp

4/15/2014, 4:19:14 AM

Confirmations

6,313,360

Merkle Root

02ac5a74a4c2da017b48be7a894830dbe5ae42d565d67708fee0dfd57f48f8a2
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.

2.098 × 10⁹⁹(100-digit number)
20980209980880098415…78220151816655522561
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
2.098 × 10⁹⁹(100-digit number)
20980209980880098415…78220151816655522561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.196 × 10⁹⁹(100-digit number)
41960419961760196831…56440303633311045121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.392 × 10⁹⁹(100-digit number)
83920839923520393663…12880607266622090241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.678 × 10¹⁰⁰(101-digit number)
16784167984704078732…25761214533244180481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.356 × 10¹⁰⁰(101-digit number)
33568335969408157465…51522429066488360961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.713 × 10¹⁰⁰(101-digit number)
67136671938816314930…03044858132976721921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.342 × 10¹⁰¹(102-digit number)
13427334387763262986…06089716265953443841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.685 × 10¹⁰¹(102-digit number)
26854668775526525972…12179432531906887681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.370 × 10¹⁰¹(102-digit number)
53709337551053051944…24358865063813775361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.074 × 10¹⁰²(103-digit number)
10741867510210610388…48717730127627550721
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:57,690,880 XPM·at block #6,805,849 · updates every 60s
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