Block #2,540,236

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 2/27/2018, 2:24:00 AM · Difficulty 10.9870 · 4,301,251 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ba3636b672333b8c53ed676ea95026fb53737e5ae65c1ae1646edb1a74258b7c

Height

#2,540,236

Difficulty

10.987032

Transactions

7

Size

19.69 KB

Version

2

Bits

0afcae23

Nonce

203,260,151

Timestamp

2/27/2018, 2:24:00 AM

Confirmations

4,301,251

Merkle Root

0a159e61034905a6a2392ee6d9a9f39d16a26c4fd87efe0012df968bebfc4132
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.

1.447 × 10⁹²(93-digit number)
14470632611579120245…88465438047137649721
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
1.447 × 10⁹²(93-digit number)
14470632611579120245…88465438047137649721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.894 × 10⁹²(93-digit number)
28941265223158240490…76930876094275299441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.788 × 10⁹²(93-digit number)
57882530446316480981…53861752188550598881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.157 × 10⁹³(94-digit number)
11576506089263296196…07723504377101197761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.315 × 10⁹³(94-digit number)
23153012178526592392…15447008754202395521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.630 × 10⁹³(94-digit number)
46306024357053184785…30894017508404791041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.261 × 10⁹³(94-digit number)
92612048714106369571…61788035016809582081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.852 × 10⁹⁴(95-digit number)
18522409742821273914…23576070033619164161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.704 × 10⁹⁴(95-digit number)
37044819485642547828…47152140067238328321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.408 × 10⁹⁴(95-digit number)
74089638971285095656…94304280134476656641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.481 × 10⁹⁵(96-digit number)
14817927794257019131…88608560268953313281
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:57,976,272 XPM·at block #6,841,486 · updates every 60s
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