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Block #74,359

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 10:40:25 AM Β· Difficulty 8.9955 Β· 6,726,533 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
63416083d0526c7cbfb8b719b21c3642eb28f503d1d47c78f4185762ec460b04
View on Chainz β†—

Height

#74,359

Difficulty

8.995458

Transactions

1

Size

201 B

Version

2

Bits

08fed64e

Nonce

1,170

Timestamp

7/21/2013, 10:40:25 AM

Confirmations

6,726,533

Mined by

⛏️ P2SHALD4vzJs4Zwqrn14ZxtLe9UeDdGRCXP6ri

Merkle Root

e6705f6748878051ad5b6db4a46cdcf2d34a898a57aef574985e948b0b2bee72
Transactions (1)
Coinbasee6705f67488780…5e948b0b2bee72
1 in β†’ 1 out12.3400 XPM110 B
ALD4vzJs…GRCXP6ri
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.

3.550 Γ— 10⁹⁢(97-digit number)
35500175823172491111…81463799667511908241
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
3.550 Γ— 10⁹⁢(97-digit number)
35500175823172491111…81463799667511908241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.100 Γ— 10⁹⁢(97-digit number)
71000351646344982223…62927599335023816481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.420 Γ— 10⁹⁷(98-digit number)
14200070329268996444…25855198670047632961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.840 Γ— 10⁹⁷(98-digit number)
28400140658537992889…51710397340095265921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.680 Γ— 10⁹⁷(98-digit number)
56800281317075985779…03420794680190531841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.136 Γ— 10⁹⁸(99-digit number)
11360056263415197155…06841589360381063681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.272 Γ— 10⁹⁸(99-digit number)
22720112526830394311…13683178720762127361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.544 Γ— 10⁹⁸(99-digit number)
45440225053660788623…27366357441524254721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.088 Γ— 10⁹⁸(99-digit number)
90880450107321577246…54732714883048509441
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:57,651,194 XPMΒ·at block #6,800,891 Β· updates every 60s
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