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Block #47,764

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/15/2013, 12:20:09 PM Β· Difficulty 8.8288 Β· 6,748,860 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
33a7c45eda5ae5887de3ceafac330643f6041b4136e48fd29fd32c66a3313335
View on Chainz β†—

Height

#47,764

Difficulty

8.828839

Transactions

1

Size

201 B

Version

2

Bits

08d42ec8

Nonce

795

Timestamp

7/15/2013, 12:20:09 PM

Confirmations

6,748,860

Mined by

⛏️ P2SHALiZQXEyqk8HnaTdtJs3ZTDkUmS4AuMz7E

Merkle Root

93b6030303f8bb52b0d3c5256b95d3bb5707e5f33db43f9160b93fc19d5aa4f2
Transactions (1)
Coinbase93b6030303f8bb…b93fc19d5aa4f2
1 in β†’ 1 out12.8100 XPM110 B
ALiZQXEy…S4AuMz7E
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.

2.915 Γ— 10⁹⁢(97-digit number)
29154761210862418864…78806298139371266229
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
2.915 Γ— 10⁹⁢(97-digit number)
29154761210862418864…78806298139371266229
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.830 Γ— 10⁹⁢(97-digit number)
58309522421724837729…57612596278742532459
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.166 Γ— 10⁹⁷(98-digit number)
11661904484344967545…15225192557485064919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.332 Γ— 10⁹⁷(98-digit number)
23323808968689935091…30450385114970129839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.664 Γ— 10⁹⁷(98-digit number)
46647617937379870183…60900770229940259679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.329 Γ— 10⁹⁷(98-digit number)
93295235874759740367…21801540459880519359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.865 Γ— 10⁹⁸(99-digit number)
18659047174951948073…43603080919761038719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.731 Γ— 10⁹⁸(99-digit number)
37318094349903896146…87206161839522077439
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 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 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,616,991 XPMΒ·at block #6,796,623 Β· updates every 60s
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