Block #2,169,979

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 6/21/2017, 6:08:56 AM · Difficulty 10.9010 · 4,661,762 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
60027bd25c6fd013a899ca71d9860af3f6b8f94d3679181d32464bbd7f0dcaa5

Height

#2,169,979

Difficulty

10.901037

Transactions

4

Size

2.01 KB

Version

2

Bits

0ae6aa55

Nonce

770,414,069

Timestamp

6/21/2017, 6:08:56 AM

Confirmations

4,661,762

Merkle Root

5b4224b878f6ea42ce631e0b56b321395d6d855264034b913550fe56143b02ca
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.

4.400 × 10⁹⁵(96-digit number)
44006795320689970977…53822746779025797119
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
4.400 × 10⁹⁵(96-digit number)
44006795320689970977…53822746779025797119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
8.801 × 10⁹⁵(96-digit number)
88013590641379941955…07645493558051594239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.760 × 10⁹⁶(97-digit number)
17602718128275988391…15290987116103188479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.520 × 10⁹⁶(97-digit number)
35205436256551976782…30581974232206376959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.041 × 10⁹⁶(97-digit number)
70410872513103953564…61163948464412753919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.408 × 10⁹⁷(98-digit number)
14082174502620790712…22327896928825507839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.816 × 10⁹⁷(98-digit number)
28164349005241581425…44655793857651015679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.632 × 10⁹⁷(98-digit number)
56328698010483162851…89311587715302031359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.126 × 10⁹⁸(99-digit number)
11265739602096632570…78623175430604062719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.253 × 10⁹⁸(99-digit number)
22531479204193265140…57246350861208125439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
4.506 × 10⁹⁸(99-digit number)
45062958408386530281…14492701722416250879
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,898,034 XPM·at block #6,831,740 · updates every 60s
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