Block #505,503

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/22/2014, 12:06:01 PM · Difficulty 10.8107 · 6,299,577 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
475f82835942326991c3de00cf89c625b8ae3b02be00bbfff0222e2ad18faa12

Height

#505,503

Difficulty

10.810684

Transactions

4

Size

5.57 KB

Version

2

Bits

0acf88f6

Nonce

92,221

Timestamp

4/22/2014, 12:06:01 PM

Confirmations

6,299,577

Merkle Root

01db1c65399ee306e681482230782aae5b83afa09078c7abc31c80041c9c412d
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.

2.197 × 10⁹⁵(96-digit number)
21976806371835878662…38191228956240405759
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
2.197 × 10⁹⁵(96-digit number)
21976806371835878662…38191228956240405759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.395 × 10⁹⁵(96-digit number)
43953612743671757324…76382457912480811519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.790 × 10⁹⁵(96-digit number)
87907225487343514648…52764915824961623039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.758 × 10⁹⁶(97-digit number)
17581445097468702929…05529831649923246079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.516 × 10⁹⁶(97-digit number)
35162890194937405859…11059663299846492159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.032 × 10⁹⁶(97-digit number)
70325780389874811718…22119326599692984319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.406 × 10⁹⁷(98-digit number)
14065156077974962343…44238653199385968639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.813 × 10⁹⁷(98-digit number)
28130312155949924687…88477306398771937279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.626 × 10⁹⁷(98-digit number)
56260624311899849375…76954612797543874559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.125 × 10⁹⁸(99-digit number)
11252124862379969875…53909225595087749119
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:57,684,704 XPM·at block #6,805,079 · updates every 60s
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