Block #2,647,207

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/3/2018, 7:36:30 PM · Difficulty 11.7564 · 4,177,296 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
916da1eb65a6e75cd175ae164e3e6a2030d0799e7db4c7bff667f00d4cf3ce9d

Height

#2,647,207

Difficulty

11.756365

Transactions

3

Size

766 B

Version

2

Bits

0bc1a128

Nonce

333,550,984

Timestamp

5/3/2018, 7:36:30 PM

Confirmations

4,177,296

Merkle Root

ce41e79ad3e10308adfd2f7627a95ecb4d6bcc397155d3855b530d3247f4eafe
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.

5.181 × 10⁹⁵(96-digit number)
51817274395530055347…77470878721378875201
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
5.181 × 10⁹⁵(96-digit number)
51817274395530055347…77470878721378875201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.036 × 10⁹⁶(97-digit number)
10363454879106011069…54941757442757750401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.072 × 10⁹⁶(97-digit number)
20726909758212022139…09883514885515500801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.145 × 10⁹⁶(97-digit number)
41453819516424044278…19767029771031001601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.290 × 10⁹⁶(97-digit number)
82907639032848088556…39534059542062003201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.658 × 10⁹⁷(98-digit number)
16581527806569617711…79068119084124006401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.316 × 10⁹⁷(98-digit number)
33163055613139235422…58136238168248012801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.632 × 10⁹⁷(98-digit number)
66326111226278470844…16272476336496025601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.326 × 10⁹⁸(99-digit number)
13265222245255694168…32544952672992051201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.653 × 10⁹⁸(99-digit number)
26530444490511388337…65089905345984102401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
5.306 × 10⁹⁸(99-digit number)
53060888981022776675…30179810691968204801
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:57,840,084 XPM·at block #6,824,502 · updates every 60s
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