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Block #74,074

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 9:19:17 AM Β· Difficulty 8.9953 Β· 6,723,375 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
86b4f289fd93e8d2d0a9b0db185b67392b4b37bdbb69058b926777f60dc46ec2
View on Chainz β†—

Height

#74,074

Difficulty

8.995261

Transactions

1

Size

203 B

Version

2

Bits

08fec975

Nonce

185

Timestamp

7/21/2013, 9:19:17 AM

Confirmations

6,723,375

Mined by

⛏️ P2SHANey87HKeHbF7P31ach44cVFqNMGUx5bYr

Merkle Root

55f7b85e0003552130ba848ebb8e13963a34c6305dd6342b0400728d0e976c2f
Transactions (1)
Coinbase55f7b85e000355…00728d0e976c2f
1 in β†’ 1 out12.3400 XPM110 B
ANey87HK…MGUx5bYr
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.

1.010 Γ— 10¹⁰²(103-digit number)
10105843132542967140…65307147241169522601
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
1.010 Γ— 10¹⁰²(103-digit number)
10105843132542967140…65307147241169522601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.021 Γ— 10¹⁰²(103-digit number)
20211686265085934280…30614294482339045201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.042 Γ— 10¹⁰²(103-digit number)
40423372530171868561…61228588964678090401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.084 Γ— 10¹⁰²(103-digit number)
80846745060343737122…22457177929356180801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.616 Γ— 10¹⁰³(104-digit number)
16169349012068747424…44914355858712361601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.233 Γ— 10¹⁰³(104-digit number)
32338698024137494849…89828711717424723201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.467 Γ— 10¹⁰³(104-digit number)
64677396048274989698…79657423434849446401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.293 Γ— 10¹⁰⁴(105-digit number)
12935479209654997939…59314846869698892801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.587 Γ— 10¹⁰⁴(105-digit number)
25870958419309995879…18629693739397785601
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:57,623,621 XPMΒ·at block #6,797,448 Β· updates every 60s
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