Block #1,452,019

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/11/2016, 4:05:15 PM · Difficulty 10.7364 · 5,387,921 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a12bda8a771229b6a2a22a81e26477e16fe128df6694cdd4750afca92d1acc7c

Height

#1,452,019

Difficulty

10.736407

Transactions

2

Size

1.11 KB

Version

2

Bits

0abc852c

Nonce

637,775,545

Timestamp

2/11/2016, 4:05:15 PM

Confirmations

5,387,921

Merkle Root

57ee29fa66ed75380e197706345d6b1a830d3ac439feb1c6c9eb94d88a0e3ad8
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.

6.006 × 10⁹⁷(98-digit number)
60061300976064442081…02308884920971960319
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
6.006 × 10⁹⁷(98-digit number)
60061300976064442081…02308884920971960319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.201 × 10⁹⁸(99-digit number)
12012260195212888416…04617769841943920639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.402 × 10⁹⁸(99-digit number)
24024520390425776832…09235539683887841279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.804 × 10⁹⁸(99-digit number)
48049040780851553665…18471079367775682559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.609 × 10⁹⁸(99-digit number)
96098081561703107330…36942158735551365119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.921 × 10⁹⁹(100-digit number)
19219616312340621466…73884317471102730239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.843 × 10⁹⁹(100-digit number)
38439232624681242932…47768634942205460479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.687 × 10⁹⁹(100-digit number)
76878465249362485864…95537269884410920959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.537 × 10¹⁰⁰(101-digit number)
15375693049872497172…91074539768821841919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.075 × 10¹⁰⁰(101-digit number)
30751386099744994345…82149079537643683839
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,963,822 XPM·at block #6,839,939 · updates every 60s
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