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Block #74,268

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 10:12:31 AM Β· Difficulty 8.9954 Β· 6,724,385 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
36f40ab52f60761543835d57c3483b50b9e681bf5b4b018efde7ea78e4e76ea8
View on Chainz β†—

Height

#74,268

Difficulty

8.995398

Transactions

1

Size

200 B

Version

2

Bits

08fed260

Nonce

273

Timestamp

7/21/2013, 10:12:31 AM

Confirmations

6,724,385

Mined by

⛏️ P2SHANey87HKeHbF7P31ach44cVFqNMGUx5bYr

Merkle Root

76aa01c04338d5262c3425c39c212a2a28f4980e68bee34b7e03c6077839cba3
Transactions (1)
Coinbase76aa01c04338d5…03c6077839cba3
1 in β†’ 1 out12.3400 XPM109 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.

6.057 Γ— 10⁹⁢(97-digit number)
60578154235157338916…58196606377591893801
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
6.057 Γ— 10⁹⁢(97-digit number)
60578154235157338916…58196606377591893801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.211 Γ— 10⁹⁷(98-digit number)
12115630847031467783…16393212755183787601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.423 Γ— 10⁹⁷(98-digit number)
24231261694062935566…32786425510367575201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.846 Γ— 10⁹⁷(98-digit number)
48462523388125871132…65572851020735150401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.692 Γ— 10⁹⁷(98-digit number)
96925046776251742265…31145702041470300801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.938 Γ— 10⁹⁸(99-digit number)
19385009355250348453…62291404082940601601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.877 Γ— 10⁹⁸(99-digit number)
38770018710500696906…24582808165881203201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.754 Γ— 10⁹⁸(99-digit number)
77540037421001393812…49165616331762406401
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,633,248 XPMΒ·at block #6,798,652 Β· updates every 60s
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