Block #2,280,566

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 9/3/2017, 10:48:08 AM · Difficulty 10.9558 · 4,550,617 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
eef593e2be68f367850e0f0ada908cb6c02f76b76c273cedbb5f778ff0f56206

Height

#2,280,566

Difficulty

10.955838

Transactions

2

Size

427 B

Version

2

Bits

0af4b1d0

Nonce

179,686,962

Timestamp

9/3/2017, 10:48:08 AM

Confirmations

4,550,617

Merkle Root

7c276739b377ead678e7e2c5bcdc596a499551f8595bb7beffb105c15c3ef002
Transactions (2)
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.

3.268 × 10⁹⁵(96-digit number)
32685282489437649468…43803882016081111041
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
3.268 × 10⁹⁵(96-digit number)
32685282489437649468…43803882016081111041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.537 × 10⁹⁵(96-digit number)
65370564978875298937…87607764032162222081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.307 × 10⁹⁶(97-digit number)
13074112995775059787…75215528064324444161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.614 × 10⁹⁶(97-digit number)
26148225991550119575…50431056128648888321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.229 × 10⁹⁶(97-digit number)
52296451983100239150…00862112257297776641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.045 × 10⁹⁷(98-digit number)
10459290396620047830…01724224514595553281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.091 × 10⁹⁷(98-digit number)
20918580793240095660…03448449029191106561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.183 × 10⁹⁷(98-digit number)
41837161586480191320…06896898058382213121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.367 × 10⁹⁷(98-digit number)
83674323172960382640…13793796116764426241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.673 × 10⁹⁸(99-digit number)
16734864634592076528…27587592233528852481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.346 × 10⁹⁸(99-digit number)
33469729269184153056…55175184467057704961
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:57,893,607 XPM·at block #6,831,182 · updates every 60s
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