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Block #75,453

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/21/2013, 4:31:43 PM Β· Difficulty 9.0043 Β· 6,731,674 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
235f4b75603cdaf632f46386be245ec8916b4b2a5ed0c404a60003bb01a77260
View on Chainz β†—

Height

#75,453

Difficulty

9.004318

Transactions

1

Size

199 B

Version

2

Bits

09011afc

Nonce

348

Timestamp

7/21/2013, 4:31:43 PM

Confirmations

6,731,674

Mined by

⛏️ P2SHAPxUMipnp1rZxF8iz1xZQD73Wi2zpbPwcA

Merkle Root

09a951c60be8468af86427f4f395934181bf47a615a0af729ee4949e6a00132f
Transactions (1)
Coinbase09a951c60be846…e4949e6a00132f
1 in β†’ 1 out12.3200 XPM110 B
APxUMipn…2zpbPwcA
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.

1.639 Γ— 10⁹³(94-digit number)
16397504292068462756…83078733622822710749
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.639 Γ— 10⁹³(94-digit number)
16397504292068462756…83078733622822710749
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.279 Γ— 10⁹³(94-digit number)
32795008584136925513…66157467245645421499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.559 Γ— 10⁹³(94-digit number)
65590017168273851027…32314934491290842999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.311 Γ— 10⁹⁴(95-digit number)
13118003433654770205…64629868982581685999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.623 Γ— 10⁹⁴(95-digit number)
26236006867309540411…29259737965163371999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.247 Γ— 10⁹⁴(95-digit number)
52472013734619080822…58519475930326743999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.049 Γ— 10⁹⁡(96-digit number)
10494402746923816164…17038951860653487999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.098 Γ— 10⁹⁡(96-digit number)
20988805493847632328…34077903721306975999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.197 Γ— 10⁹⁡(96-digit number)
41977610987695264657…68155807442613951999
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,701,120 XPMΒ·at block #6,807,126 Β· updates every 60s
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