Block #2,642,660

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/1/2018, 7:44:33 PM · Difficulty 11.6600 · 4,188,109 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d868058d5c73520a56eb979121f36f893f98c599a0e8815cca8e8a89111ab11b

Height

#2,642,660

Difficulty

11.659991

Transactions

3

Size

1.65 KB

Version

2

Bits

0ba8f530

Nonce

260,091,354

Timestamp

5/1/2018, 7:44:33 PM

Confirmations

4,188,109

Merkle Root

e01b8a47bc636b2a19194b4ce28061c93133d99117a945d512bfece78bc25ddd
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.

2.284 × 10⁹⁶(97-digit number)
22843894703562946590…91170798983383623681
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
2.284 × 10⁹⁶(97-digit number)
22843894703562946590…91170798983383623681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.568 × 10⁹⁶(97-digit number)
45687789407125893181…82341597966767247361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.137 × 10⁹⁶(97-digit number)
91375578814251786363…64683195933534494721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.827 × 10⁹⁷(98-digit number)
18275115762850357272…29366391867068989441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.655 × 10⁹⁷(98-digit number)
36550231525700714545…58732783734137978881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.310 × 10⁹⁷(98-digit number)
73100463051401429090…17465567468275957761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.462 × 10⁹⁸(99-digit number)
14620092610280285818…34931134936551915521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.924 × 10⁹⁸(99-digit number)
29240185220560571636…69862269873103831041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.848 × 10⁹⁸(99-digit number)
58480370441121143272…39724539746207662081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.169 × 10⁹⁹(100-digit number)
11696074088224228654…79449079492415324161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.339 × 10⁹⁹(100-digit number)
23392148176448457309…58898158984830648321
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:57,890,288 XPM·at block #6,830,768 · updates every 60s
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