Block #2,127,706

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/22/2017, 4:44:13 AM · Difficulty 10.9180 · 4,706,019 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
82838d54060555a6430de1c2183edd0ba3ff5b55aac69942fdcd2aaababdcd44

Height

#2,127,706

Difficulty

10.917962

Transactions

2

Size

426 B

Version

2

Bits

0aeaff87

Nonce

1,006,702,787

Timestamp

5/22/2017, 4:44:13 AM

Confirmations

4,706,019

Merkle Root

0e960183b5bf8ff9deca2696f3e4ed4d9907bb30d3a1101bf188eb75de3ba81c
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.

4.206 × 10⁹³(94-digit number)
42063193800000585920…75404302848539383761
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
4.206 × 10⁹³(94-digit number)
42063193800000585920…75404302848539383761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.412 × 10⁹³(94-digit number)
84126387600001171841…50808605697078767521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.682 × 10⁹⁴(95-digit number)
16825277520000234368…01617211394157535041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.365 × 10⁹⁴(95-digit number)
33650555040000468736…03234422788315070081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.730 × 10⁹⁴(95-digit number)
67301110080000937473…06468845576630140161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.346 × 10⁹⁵(96-digit number)
13460222016000187494…12937691153260280321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.692 × 10⁹⁵(96-digit number)
26920444032000374989…25875382306520560641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.384 × 10⁹⁵(96-digit number)
53840888064000749978…51750764613041121281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.076 × 10⁹⁶(97-digit number)
10768177612800149995…03501529226082242561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.153 × 10⁹⁶(97-digit number)
21536355225600299991…07003058452164485121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
4.307 × 10⁹⁶(97-digit number)
43072710451200599982…14006116904328970241
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:57,914,022 XPM·at block #6,833,724 · updates every 60s
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