Block #2,924,381

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 11/15/2018, 6:40:18 PM · Difficulty 11.3602 · 3,916,850 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c1da22d6360a1a9beca1c61a35e9c17c63ebeec1df4f9aedc9a0715c3257a356

Height

#2,924,381

Difficulty

11.360163

Transactions

2

Size

539 B

Version

2

Bits

0b5c33aa

Nonce

615,564,934

Timestamp

11/15/2018, 6:40:18 PM

Confirmations

3,916,850

Merkle Root

839f177325f0024863f08b3a1a4c24d4a063634723f51fa4499b42db66f998c7
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.

1.377 × 10⁹⁵(96-digit number)
13776884008691333399…35755170812367188551
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
1.377 × 10⁹⁵(96-digit number)
13776884008691333399…35755170812367188551
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.755 × 10⁹⁵(96-digit number)
27553768017382666798…71510341624734377101
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.510 × 10⁹⁵(96-digit number)
55107536034765333596…43020683249468754201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.102 × 10⁹⁶(97-digit number)
11021507206953066719…86041366498937508401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.204 × 10⁹⁶(97-digit number)
22043014413906133438…72082732997875016801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.408 × 10⁹⁶(97-digit number)
44086028827812266877…44165465995750033601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.817 × 10⁹⁶(97-digit number)
88172057655624533754…88330931991500067201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.763 × 10⁹⁷(98-digit number)
17634411531124906750…76661863983000134401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.526 × 10⁹⁷(98-digit number)
35268823062249813501…53323727966000268801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.053 × 10⁹⁷(98-digit number)
70537646124499627003…06647455932000537601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.410 × 10⁹⁸(99-digit number)
14107529224899925400…13294911864001075201
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:57,974,207 XPM·at block #6,841,230 · updates every 60s
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