Block #2,950,896

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 12/3/2018, 11:53:36 PM · Difficulty 11.3958 · 3,892,749 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f75df3ce2f30fbf4ac989ffe7b2d5174bb5cc10fe1e9e43cdf4643bd312d39e3

Height

#2,950,896

Difficulty

11.395845

Transactions

4

Size

1.70 KB

Version

2

Bits

0b65561f

Nonce

678,089,922

Timestamp

12/3/2018, 11:53:36 PM

Confirmations

3,892,749

Merkle Root

a95fc5f39806f288860693caf4ba5030b756b36adb3a7a6126b1de057e3f05bf
Transactions (4)
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.

9.467 × 10⁹⁵(96-digit number)
94674558224845711428…34338754113913528321
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
9.467 × 10⁹⁵(96-digit number)
94674558224845711428…34338754113913528321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.893 × 10⁹⁶(97-digit number)
18934911644969142285…68677508227827056641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.786 × 10⁹⁶(97-digit number)
37869823289938284571…37355016455654113281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.573 × 10⁹⁶(97-digit number)
75739646579876569142…74710032911308226561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.514 × 10⁹⁷(98-digit number)
15147929315975313828…49420065822616453121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.029 × 10⁹⁷(98-digit number)
30295858631950627657…98840131645232906241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.059 × 10⁹⁷(98-digit number)
60591717263901255314…97680263290465812481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.211 × 10⁹⁸(99-digit number)
12118343452780251062…95360526580931624961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.423 × 10⁹⁸(99-digit number)
24236686905560502125…90721053161863249921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.847 × 10⁹⁸(99-digit number)
48473373811121004251…81442106323726499841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
9.694 × 10⁹⁸(99-digit number)
96946747622242008502…62884212647452999681
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:57,993,530 XPM·at block #6,843,644 · updates every 60s
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