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Block #82,274

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/25/2013, 7:36:37 AM Β· Difficulty 9.2755 Β· 6,714,096 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
65c575cd3b4c7b3e2f93ef74a88d9becfae88b1dfed9b03a71a2a5deaaa49411
View on Chainz β†—

Height

#82,274

Difficulty

9.275494

Transactions

1

Size

203 B

Version

2

Bits

094686be

Nonce

107,744

Timestamp

7/25/2013, 7:36:37 AM

Confirmations

6,714,096

Mined by

⛏️ P2SHAHGi8wDB5Q1pnktV2RKKJj33qeeKomrPdd

Merkle Root

e4d7370615985f2b271688abf18a06e9439156a6d227b2b7f92ede518fde3711
Transactions (1)
Coinbasee4d7370615985f…2ede518fde3711
1 in β†’ 1 out11.6100 XPM109 B
AHGi8wDB…eKomrPdd
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.

2.467 Γ— 10¹⁰⁡(106-digit number)
24671093307754076687…60551892445630855851
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
2.467 Γ— 10¹⁰⁡(106-digit number)
24671093307754076687…60551892445630855851
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.934 Γ— 10¹⁰⁡(106-digit number)
49342186615508153375…21103784891261711701
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.868 Γ— 10¹⁰⁡(106-digit number)
98684373231016306750…42207569782523423401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.973 Γ— 10¹⁰⁢(107-digit number)
19736874646203261350…84415139565046846801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.947 Γ— 10¹⁰⁢(107-digit number)
39473749292406522700…68830279130093693601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.894 Γ— 10¹⁰⁢(107-digit number)
78947498584813045400…37660558260187387201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.578 Γ— 10¹⁰⁷(108-digit number)
15789499716962609080…75321116520374774401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.157 Γ— 10¹⁰⁷(108-digit number)
31578999433925218160…50642233040749548801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.315 Γ— 10¹⁰⁷(108-digit number)
63157998867850436320…01284466081499097601
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:57,614,954 XPMΒ·at block #6,796,369 Β· updates every 60s
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