Block #2,702,320

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 6/12/2018, 1:54:19 PM · Difficulty 11.6294 · 4,130,790 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2f89701ca84e39c4d64b9168504c5c725ab625b448b71d8268bb7fbb7baed472

Height

#2,702,320

Difficulty

11.629373

Transactions

3

Size

650 B

Version

2

Bits

0ba11e8f

Nonce

615,454,695

Timestamp

6/12/2018, 1:54:19 PM

Confirmations

4,130,790

Merkle Root

df1ea3e12182e887a73262b99176a3e538083b4c56dc46e86c8dab02b01391d2
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.

2.888 × 10⁹²(93-digit number)
28889396499213176730…34528761917770848321
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
2.888 × 10⁹²(93-digit number)
28889396499213176730…34528761917770848321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.777 × 10⁹²(93-digit number)
57778792998426353460…69057523835541696641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.155 × 10⁹³(94-digit number)
11555758599685270692…38115047671083393281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.311 × 10⁹³(94-digit number)
23111517199370541384…76230095342166786561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.622 × 10⁹³(94-digit number)
46223034398741082768…52460190684333573121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.244 × 10⁹³(94-digit number)
92446068797482165536…04920381368667146241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.848 × 10⁹⁴(95-digit number)
18489213759496433107…09840762737334292481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.697 × 10⁹⁴(95-digit number)
36978427518992866214…19681525474668584961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.395 × 10⁹⁴(95-digit number)
73956855037985732429…39363050949337169921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.479 × 10⁹⁵(96-digit number)
14791371007597146485…78726101898674339841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.958 × 10⁹⁵(96-digit number)
29582742015194292971…57452203797348679681
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:57,909,055 XPM·at block #6,833,109 · updates every 60s
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