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Block #308,549

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/13/2013, 4:02:56 AM Β· Difficulty 9.9945 Β· 6,518,208 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9e4ea896a1e83d00dda1693817e19771011c36154813e0be636505259eb1749a
View on Chainz β†—

Height

#308,549

Difficulty

9.994538

Transactions

2

Size

721 B

Version

2

Bits

09fe9a04

Nonce

1,490

Timestamp

12/13/2013, 4:02:56 AM

Confirmations

6,518,208

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

dcf6b82ec1cdb066e7c4df0d6228390feee605688c216edcf96cbfc0909a4899
Transactions (2)
Coinbase171b61e9618c68…27d91ceb2eca78
1 in β†’ 1 out10.0100 XPM110 B
AeKNrjNj…1NEq95Ta
cda0128fbc783e…ce0fea4e6c85cf
3 in β†’ 2 out12.7610 XPM522 B
ALhwi2NY…Vg8FiXDKAYChGm3w…CfL9PEgK
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.

2.608 Γ— 10⁹³(94-digit number)
26089216872842510066…75073532356323379199
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
2.608 Γ— 10⁹³(94-digit number)
26089216872842510066…75073532356323379199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.217 Γ— 10⁹³(94-digit number)
52178433745685020132…50147064712646758399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.043 Γ— 10⁹⁴(95-digit number)
10435686749137004026…00294129425293516799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.087 Γ— 10⁹⁴(95-digit number)
20871373498274008052…00588258850587033599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.174 Γ— 10⁹⁴(95-digit number)
41742746996548016105…01176517701174067199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.348 Γ— 10⁹⁴(95-digit number)
83485493993096032211…02353035402348134399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.669 Γ— 10⁹⁡(96-digit number)
16697098798619206442…04706070804696268799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.339 Γ— 10⁹⁡(96-digit number)
33394197597238412884…09412141609392537599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.678 Γ— 10⁹⁡(96-digit number)
66788395194476825769…18824283218785075199
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:57,858,214 XPMΒ·at block #6,826,756 Β· updates every 60s
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