Block #2,673,226

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 5/22/2018, 4:20:43 PM · Difficulty 11.6951 · 4,159,637 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4344dcfc5452d656215daaad5ccb079cb7fa1fee72e3febfa9d87f955cf24520

Height

#2,673,226

Difficulty

11.695078

Transactions

2

Size

724 B

Version

2

Bits

0bb1f0a0

Nonce

104,366,816

Timestamp

5/22/2018, 4:20:43 PM

Confirmations

4,159,637

Merkle Root

47b78e9ae9cce07efb7c01ce6731a5f9c9550d9f03a94b1b95a03a24cf0b31c3
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.

7.031 × 10⁹⁶(97-digit number)
70311131916832441064…56318683842333148159
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
7.031 × 10⁹⁶(97-digit number)
70311131916832441064…56318683842333148159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.406 × 10⁹⁷(98-digit number)
14062226383366488212…12637367684666296319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.812 × 10⁹⁷(98-digit number)
28124452766732976425…25274735369332592639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.624 × 10⁹⁷(98-digit number)
56248905533465952851…50549470738665185279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.124 × 10⁹⁸(99-digit number)
11249781106693190570…01098941477330370559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.249 × 10⁹⁸(99-digit number)
22499562213386381140…02197882954660741119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.499 × 10⁹⁸(99-digit number)
44999124426772762281…04395765909321482239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
8.999 × 10⁹⁸(99-digit number)
89998248853545524562…08791531818642964479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.799 × 10⁹⁹(100-digit number)
17999649770709104912…17583063637285928959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.599 × 10⁹⁹(100-digit number)
35999299541418209824…35166127274571857919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
7.199 × 10⁹⁹(100-digit number)
71998599082836419649…70332254549143715839
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:57,907,073 XPM·at block #6,832,862 · updates every 60s
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