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Block #253,818

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/10/2013, 9:03:37 AM Β· Difficulty 9.9725 Β· 6,582,874 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
56f00ef6725982b3070b7dd44e69459769e46da72dbeb86a43345d3bd31acf9b
View on Chainz β†—

Height

#253,818

Difficulty

9.972499

Transactions

1

Size

208 B

Version

2

Bits

09f8f5b3

Nonce

181,200

Timestamp

11/10/2013, 9:03:37 AM

Confirmations

6,582,874

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

6fd881522f4069a5db48435cf533bf4ddb9497fc43a74d43a89dbe8dd170f33d
Transactions (1)
Coinbase6fd881522f4069…9dbe8dd170f33d
1 in β†’ 1 out10.0400 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.008 Γ— 10⁹⁹(100-digit number)
10085753913811439663…80550156262383513601
Discovered Prime Numbers
p_k = 2^k Γ— 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
1.008 Γ— 10⁹⁹(100-digit number)
10085753913811439663…80550156262383513601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.017 Γ— 10⁹⁹(100-digit number)
20171507827622879327…61100312524767027201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.034 Γ— 10⁹⁹(100-digit number)
40343015655245758655…22200625049534054401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.068 Γ— 10⁹⁹(100-digit number)
80686031310491517311…44401250099068108801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.613 Γ— 10¹⁰⁰(101-digit number)
16137206262098303462…88802500198136217601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.227 Γ— 10¹⁰⁰(101-digit number)
32274412524196606924…77605000396272435201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.454 Γ— 10¹⁰⁰(101-digit number)
64548825048393213848…55210000792544870401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.290 Γ— 10¹⁰¹(102-digit number)
12909765009678642769…10420001585089740801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.581 Γ— 10¹⁰¹(102-digit number)
25819530019357285539…20840003170179481601
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,937,816 XPMΒ·at block #6,836,691 Β· updates every 60s
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