Block #2,672,117

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 5/21/2018, 10:35:59 PM · Difficulty 11.6923 · 4,165,055 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
90f62db437938b7f0b7d3f4646d28f364a6bac20e84ca7d339c7a498a16bc272

Height

#2,672,117

Difficulty

11.692278

Transactions

2

Size

723 B

Version

2

Bits

0bb13924

Nonce

837,287,866

Timestamp

5/21/2018, 10:35:59 PM

Confirmations

4,165,055

Merkle Root

20f6d79be3044035f95a1903acbb2fcbb3dc00f840bc9f75ca4c9a174f216836
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.

1.531 × 10⁹⁴(95-digit number)
15315880115720114889…95427287244009616999
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
1.531 × 10⁹⁴(95-digit number)
15315880115720114889…95427287244009616999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.063 × 10⁹⁴(95-digit number)
30631760231440229779…90854574488019233999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.126 × 10⁹⁴(95-digit number)
61263520462880459558…81709148976038467999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.225 × 10⁹⁵(96-digit number)
12252704092576091911…63418297952076935999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.450 × 10⁹⁵(96-digit number)
24505408185152183823…26836595904153871999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.901 × 10⁹⁵(96-digit number)
49010816370304367647…53673191808307743999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
9.802 × 10⁹⁵(96-digit number)
98021632740608735294…07346383616615487999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.960 × 10⁹⁶(97-digit number)
19604326548121747058…14692767233230975999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.920 × 10⁹⁶(97-digit number)
39208653096243494117…29385534466461951999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.841 × 10⁹⁶(97-digit number)
78417306192486988235…58771068932923903999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.568 × 10⁹⁷(98-digit number)
15683461238497397647…17542137865847807999
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:57,941,690 XPM·at block #6,837,171 · updates every 60s
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