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Block #85,144

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/27/2013, 6:26:44 AM Β· Difficulty 9.2843 Β· 6,717,506 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cc69217fbf58c204da80f895d36365352bc83f731657cc9c5a6f57f7bddfd67d
View on Chainz β†—

Height

#85,144

Difficulty

9.284329

Transactions

1

Size

201 B

Version

2

Bits

0948c9c8

Nonce

366,741

Timestamp

7/27/2013, 6:26:44 AM

Confirmations

6,717,506

Mined by

⛏️ P2SHASXW8s4r1QTq8Djg6zDrh4WCnULM8vqY9U

Merkle Root

9be9f1345a118e7ff02a284c9ac4671ed2513141644bd784355ee1cfe445db55
Transactions (1)
Coinbase9be9f1345a118e…5ee1cfe445db55
1 in β†’ 1 out11.5800 XPM109 B
ASXW8s4r…LM8vqY9U
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.

3.221 Γ— 10⁹⁸(99-digit number)
32217957042195407364…18784106352657212001
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
3.221 Γ— 10⁹⁸(99-digit number)
32217957042195407364…18784106352657212001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.443 Γ— 10⁹⁸(99-digit number)
64435914084390814728…37568212705314424001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.288 Γ— 10⁹⁹(100-digit number)
12887182816878162945…75136425410628848001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.577 Γ— 10⁹⁹(100-digit number)
25774365633756325891…50272850821257696001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.154 Γ— 10⁹⁹(100-digit number)
51548731267512651782…00545701642515392001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.030 Γ— 10¹⁰⁰(101-digit number)
10309746253502530356…01091403285030784001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.061 Γ— 10¹⁰⁰(101-digit number)
20619492507005060713…02182806570061568001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.123 Γ— 10¹⁰⁰(101-digit number)
41238985014010121426…04365613140123136001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.247 Γ— 10¹⁰⁰(101-digit number)
82477970028020242852…08731226280246272001
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:57,665,216 XPMΒ·at block #6,802,649 Β· updates every 60s
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