Block #2,488,062

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/24/2018, 1:34:53 PM · Difficulty 10.9696 · 4,355,882 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
19c0d9597da94c20880913de9a11900c11687f0eae71ee61d0d7220182ba2f64

Height

#2,488,062

Difficulty

10.969591

Transactions

3

Size

653 B

Version

2

Bits

0af83721

Nonce

1,089,100,608

Timestamp

1/24/2018, 1:34:53 PM

Confirmations

4,355,882

Merkle Root

f7ab39e08761b16fff3d9103c53a4f231abe22f68ff396d20863ee8be624de69
Transactions (3)
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.

1.826 × 10⁹⁶(97-digit number)
18269262029374889516…36032186968129896961
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
1.826 × 10⁹⁶(97-digit number)
18269262029374889516…36032186968129896961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.653 × 10⁹⁶(97-digit number)
36538524058749779032…72064373936259793921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.307 × 10⁹⁶(97-digit number)
73077048117499558065…44128747872519587841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.461 × 10⁹⁷(98-digit number)
14615409623499911613…88257495745039175681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.923 × 10⁹⁷(98-digit number)
29230819246999823226…76514991490078351361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.846 × 10⁹⁷(98-digit number)
58461638493999646452…53029982980156702721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.169 × 10⁹⁸(99-digit number)
11692327698799929290…06059965960313405441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.338 × 10⁹⁸(99-digit number)
23384655397599858581…12119931920626810881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.676 × 10⁹⁸(99-digit number)
46769310795199717162…24239863841253621761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.353 × 10⁹⁸(99-digit number)
93538621590399434324…48479727682507243521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.870 × 10⁹⁹(100-digit number)
18707724318079886864…96959455365014487041
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:57,995,926 XPM·at block #6,843,943 · updates every 60s
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