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Block #54,373

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/16/2013, 8:07:08 PM Β· Difficulty 8.9328 Β· 6,755,562 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4d34d2c918a95ddbb6b88c03c2abe0a3eda787c69a7e8eb3dedae2506e26bb67
View on Chainz β†—

Height

#54,373

Difficulty

8.932791

Transactions

2

Size

358 B

Version

2

Bits

08eecb69

Nonce

37

Timestamp

7/16/2013, 8:07:08 PM

Confirmations

6,755,562

Mined by

⛏️ P2SHAGDtP8Skh6DMqLEoZTYbd3ujcikC5TcryM

Merkle Root

e2c9be5dbb83525b7d00042e3f445fc6580bfa31683f2d049c57cd41067ee37e
Transactions (2)
Coinbase181814c47609f1…39ac8fa29fb8db
1 in β†’ 1 out12.5200 XPM110 B
AGDtP8Sk…kC5TcryM
a99b8af09593d1…1e1fa7157127b0
1 in β†’ 1 out12.6700 XPM159 B
AVXpXMS3…dbsyn72W
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.

3.221 Γ— 10⁹³(94-digit number)
32218059359943130646…64747627363922450139
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
3.221 Γ— 10⁹³(94-digit number)
32218059359943130646…64747627363922450139
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.443 Γ— 10⁹³(94-digit number)
64436118719886261292…29495254727844900279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.288 Γ— 10⁹⁴(95-digit number)
12887223743977252258…58990509455689800559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.577 Γ— 10⁹⁴(95-digit number)
25774447487954504516…17981018911379601119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.154 Γ— 10⁹⁴(95-digit number)
51548894975909009033…35962037822759202239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.030 Γ— 10⁹⁡(96-digit number)
10309778995181801806…71924075645518404479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.061 Γ— 10⁹⁡(96-digit number)
20619557990363603613…43848151291036808959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.123 Γ— 10⁹⁡(96-digit number)
41239115980727207227…87696302582073617919
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:57,723,567 XPMΒ·at block #6,809,934 Β· updates every 60s
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