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Block #468,460

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/31/2014, 12:54:48 PM Β· Difficulty 10.4307 Β· 6,335,069 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8e3a4008022f356a676b6671ad3c4ce798e19c52424d30b142ea72f81a139888
View on Chainz β†—

Height

#468,460

Difficulty

10.430736

Transactions

3

Size

3.75 KB

Version

2

Bits

0a6e44bb

Nonce

234,265

Timestamp

3/31/2014, 12:54:48 PM

Confirmations

6,335,069

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

4d018f5b4fa67846c9f7f1af06435284ccdb446c69649aa1ca493c1d3a720ec4
Transactions (3)
Coinbase6b9a48f030ca32…8fda76101ea2fa
1 in β†’ 1 out9.2300 XPM110 B
AeKNrjNj…1NEq95Ta
d9a3e04f6b9627…d03c690f76bad1
23 in β†’ 1 out70.5554 XPM3.36 KB
AYE3M8Zj…Q1AfobwT
722b15f46c022c…99bc7309e45ee6
1 in β†’ 1 out2.9943 XPM193 B
AZRjMKU3…gB4Pp7tQ
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.

1.398 Γ— 10¹⁰³(104-digit number)
13981600514960377963…88954853875271360649
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
1.398 Γ— 10¹⁰³(104-digit number)
13981600514960377963…88954853875271360649
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.796 Γ— 10¹⁰³(104-digit number)
27963201029920755926…77909707750542721299
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.592 Γ— 10¹⁰³(104-digit number)
55926402059841511852…55819415501085442599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.118 Γ— 10¹⁰⁴(105-digit number)
11185280411968302370…11638831002170885199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.237 Γ— 10¹⁰⁴(105-digit number)
22370560823936604740…23277662004341770399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.474 Γ— 10¹⁰⁴(105-digit number)
44741121647873209481…46555324008683540799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.948 Γ— 10¹⁰⁴(105-digit number)
89482243295746418963…93110648017367081599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.789 Γ— 10¹⁰⁡(106-digit number)
17896448659149283792…86221296034734163199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.579 Γ— 10¹⁰⁡(106-digit number)
35792897318298567585…72442592069468326399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.158 Γ— 10¹⁰⁡(106-digit number)
71585794636597135170…44885184138936652799
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:57,672,260 XPMΒ·at block #6,803,528 Β· updates every 60s
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