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Block #74,945

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 1:50:23 PM Β· Difficulty 8.9958 Β· 6,724,335 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b2fd21e8634716c9324c72b21da92ef41742bdfcebe0c27bf4e3197eeb5af519
View on Chainz β†—

Height

#74,945

Difficulty

8.995818

Transactions

1

Size

199 B

Version

2

Bits

08feedef

Nonce

566

Timestamp

7/21/2013, 1:50:23 PM

Confirmations

6,724,335

Mined by

⛏️ P2SHAKZxB9sLnFagacwoGg9Nd9LCvLZhxs5zB5

Merkle Root

8d6c385e983559ccb653b2b84cb0b4d63a7546042868ea201ed7675fe0ac9b22
Transactions (1)
Coinbase8d6c385e983559…d7675fe0ac9b22
1 in β†’ 1 out12.3400 XPM110 B
AKZxB9sL…Zhxs5zB5
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.

2.505 Γ— 10⁹³(94-digit number)
25054582240046835255…28618983468463288201
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
2.505 Γ— 10⁹³(94-digit number)
25054582240046835255…28618983468463288201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.010 Γ— 10⁹³(94-digit number)
50109164480093670511…57237966936926576401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.002 Γ— 10⁹⁴(95-digit number)
10021832896018734102…14475933873853152801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.004 Γ— 10⁹⁴(95-digit number)
20043665792037468204…28951867747706305601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.008 Γ— 10⁹⁴(95-digit number)
40087331584074936408…57903735495412611201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.017 Γ— 10⁹⁴(95-digit number)
80174663168149872817…15807470990825222401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.603 Γ— 10⁹⁡(96-digit number)
16034932633629974563…31614941981650444801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.206 Γ— 10⁹⁡(96-digit number)
32069865267259949127…63229883963300889601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.413 Γ— 10⁹⁡(96-digit number)
64139730534519898254…26459767926601779201
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:57,638,281 XPMΒ·at block #6,799,279 Β· updates every 60s
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