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Block #52,552

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/16/2013, 10:53:16 AM Β· Difficulty 8.9135 Β· 6,756,462 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9d2609012d125f22b9880707e925713b53ebf7523ecd74516b860ee9bfc9d3f0
View on Chainz β†—

Height

#52,552

Difficulty

8.913510

Transactions

1

Size

201 B

Version

2

Bits

08e9dbc7

Nonce

0

Timestamp

7/16/2013, 10:53:16 AM

Confirmations

6,756,462

Mined by

⛏️ P2SHAL9vapsHqBtuDx7zu17DTNc7U8omkJkqF8

Merkle Root

c9cb474278431df812d1657020cb46db198d26c5781e18721f01bbcdd2cd3d64
Transactions (1)
Coinbasec9cb474278431d…01bbcdd2cd3d64
1 in β†’ 1 out12.5700 XPM110 B
AL9vapsH…omkJkqF8
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.466 Γ— 10⁹⁢(97-digit number)
44668323213362854341…31684259674079350499
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
4.466 Γ— 10⁹⁢(97-digit number)
44668323213362854341…31684259674079350499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.933 Γ— 10⁹⁢(97-digit number)
89336646426725708682…63368519348158700999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.786 Γ— 10⁹⁷(98-digit number)
17867329285345141736…26737038696317401999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.573 Γ— 10⁹⁷(98-digit number)
35734658570690283472…53474077392634803999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.146 Γ— 10⁹⁷(98-digit number)
71469317141380566945…06948154785269607999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.429 Γ— 10⁹⁸(99-digit number)
14293863428276113389…13896309570539215999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.858 Γ— 10⁹⁸(99-digit number)
28587726856552226778…27792619141078431999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.717 Γ— 10⁹⁸(99-digit number)
57175453713104453556…55585238282156863999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.143 Γ— 10⁹⁹(100-digit number)
11435090742620890711…11170476564313727999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,716,173 XPMΒ·at block #6,809,013 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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