Block #1,222,289

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 9/4/2015, 9:58:29 PM · Difficulty 10.7415 · 5,583,801 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
261590935b2d983bd13be75aa6b661ae4bc06442046ec87a1c9c5cfe491a3cbc

Height

#1,222,289

Difficulty

10.741477

Transactions

2

Size

580 B

Version

2

Bits

0abdd171

Nonce

902,883,142

Timestamp

9/4/2015, 9:58:29 PM

Confirmations

5,583,801

Merkle Root

392e60282af8a87267ec9e29f4719f2d7399b92b6ab8a89fadfa421bc5f40db8
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.

1.410 × 10⁹⁵(96-digit number)
14109664966243837354…01659941310456056319
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
1.410 × 10⁹⁵(96-digit number)
14109664966243837354…01659941310456056319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.821 × 10⁹⁵(96-digit number)
28219329932487674708…03319882620912112639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.643 × 10⁹⁵(96-digit number)
56438659864975349417…06639765241824225279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.128 × 10⁹⁶(97-digit number)
11287731972995069883…13279530483648450559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.257 × 10⁹⁶(97-digit number)
22575463945990139766…26559060967296901119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.515 × 10⁹⁶(97-digit number)
45150927891980279533…53118121934593802239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
9.030 × 10⁹⁶(97-digit number)
90301855783960559067…06236243869187604479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.806 × 10⁹⁷(98-digit number)
18060371156792111813…12472487738375208959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.612 × 10⁹⁷(98-digit number)
36120742313584223626…24944975476750417919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.224 × 10⁹⁷(98-digit number)
72241484627168447253…49889950953500835839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.444 × 10⁹⁸(99-digit number)
14448296925433689450…99779901907001671679
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:57,692,792 XPM·at block #6,806,089 · updates every 60s
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