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Block #624,540

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/9/2014, 2:59:39 AM Β· Difficulty 10.9584 Β· 6,200,483 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
912ac4dc9706b183136cd1a48545e90fc6a99a35d5dfd240397329e6e7a8edb8
View on Chainz β†—

Height

#624,540

Difficulty

10.958368

Transactions

1

Size

200 B

Version

2

Bits

0af55799

Nonce

156,459

Timestamp

7/9/2014, 2:59:39 AM

Confirmations

6,200,483

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

057e8fa6ab75672b1277171fcd3fe625d4677090e1acf19f43929c404a3da018
Transactions (1)
Coinbase057e8fa6ab7567…929c404a3da018
1 in β†’ 1 out8.3100 XPM110 B
AeKNrjNj…1NEq95Ta
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.

1.631 Γ— 10⁹⁡(96-digit number)
16312987899841438545…36271189900512625679
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
1.631 Γ— 10⁹⁡(96-digit number)
16312987899841438545…36271189900512625679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.262 Γ— 10⁹⁡(96-digit number)
32625975799682877090…72542379801025251359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.525 Γ— 10⁹⁡(96-digit number)
65251951599365754180…45084759602050502719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.305 Γ— 10⁹⁢(97-digit number)
13050390319873150836…90169519204101005439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.610 Γ— 10⁹⁢(97-digit number)
26100780639746301672…80339038408202010879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.220 Γ— 10⁹⁢(97-digit number)
52201561279492603344…60678076816404021759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.044 Γ— 10⁹⁷(98-digit number)
10440312255898520668…21356153632808043519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.088 Γ— 10⁹⁷(98-digit number)
20880624511797041337…42712307265616087039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.176 Γ— 10⁹⁷(98-digit number)
41761249023594082675…85424614531232174079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.352 Γ— 10⁹⁷(98-digit number)
83522498047188165351…70849229062464348159
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,844,267 XPMΒ·at block #6,825,022 Β· updates every 60s
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