Block #484,273

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/10/2014, 11:37:25 AM · Difficulty 10.5822 · 6,328,728 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f38dd82e8da5bb5e814b360c10db278f184f994f20094e52c65c27f12d58f515

Height

#484,273

Difficulty

10.582187

Transactions

1

Size

802 B

Version

2

Bits

0a950a3b

Nonce

174

Timestamp

4/10/2014, 11:37:25 AM

Confirmations

6,328,728

Merkle Root

dddedb16feae6ba4c2d0d5038dddd6dafa79daff29a4731b104d5632ad5c77ea
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.

2.492 × 10¹⁰²(103-digit number)
24923854978223568582…19960554344991139841
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
2.492 × 10¹⁰²(103-digit number)
24923854978223568582…19960554344991139841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.984 × 10¹⁰²(103-digit number)
49847709956447137164…39921108689982279681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.969 × 10¹⁰²(103-digit number)
99695419912894274328…79842217379964559361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.993 × 10¹⁰³(104-digit number)
19939083982578854865…59684434759929118721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.987 × 10¹⁰³(104-digit number)
39878167965157709731…19368869519858237441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.975 × 10¹⁰³(104-digit number)
79756335930315419462…38737739039716474881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.595 × 10¹⁰⁴(105-digit number)
15951267186063083892…77475478079432949761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.190 × 10¹⁰⁴(105-digit number)
31902534372126167785…54950956158865899521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.380 × 10¹⁰⁴(105-digit number)
63805068744252335570…09901912317731799041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.276 × 10¹⁰⁵(106-digit number)
12761013748850467114…19803824635463598081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.552 × 10¹⁰⁵(106-digit number)
25522027497700934228…39607649270927196161
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,748,048 XPM·at block #6,813,000 · updates every 60s
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