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Block #73,333

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 5:17:48 AM Β· Difficulty 8.9947 Β· 6,744,436 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7d150b424b661be161beee9a4fde55ea5669b2079c3a3e1bd1fd5fcf9ad32f8c
View on Chainz β†—

Height

#73,333

Difficulty

8.994745

Transactions

1

Size

204 B

Version

2

Bits

08fea79a

Nonce

266

Timestamp

7/21/2013, 5:17:48 AM

Confirmations

6,744,436

Mined by

⛏️ P2SHAH7Eh9GYMSnm23owcXVdfkeuiPK86X1CDg

Merkle Root

b8ba683a335f6dec165f37ec73f0d483e9fb197d5486dd6db375917088a5712b
Transactions (1)
Coinbaseb8ba683a335f6d…75917088a5712b
1 in β†’ 1 out12.3400 XPM110 B
AH7Eh9GY…K86X1CDg
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.

5.171 Γ— 10¹⁰³(104-digit number)
51712977472014396944…03770645502494622481
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
5.171 Γ— 10¹⁰³(104-digit number)
51712977472014396944…03770645502494622481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.034 Γ— 10¹⁰⁴(105-digit number)
10342595494402879388…07541291004989244961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.068 Γ— 10¹⁰⁴(105-digit number)
20685190988805758777…15082582009978489921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.137 Γ— 10¹⁰⁴(105-digit number)
41370381977611517555…30165164019956979841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.274 Γ— 10¹⁰⁴(105-digit number)
82740763955223035111…60330328039913959681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.654 Γ— 10¹⁰⁡(106-digit number)
16548152791044607022…20660656079827919361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.309 Γ— 10¹⁰⁡(106-digit number)
33096305582089214044…41321312159655838721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.619 Γ— 10¹⁰⁡(106-digit number)
66192611164178428089…82642624319311677441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.323 Γ— 10¹⁰⁢(107-digit number)
13238522232835685617…65285248638623354881
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:57,786,209 XPMΒ·at block #6,817,768 Β· updates every 60s
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