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Block #339,826

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/2/2014, 9:02:13 AM Β· Difficulty 10.1299 Β· 6,455,726 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
594f48b114d3282389f5ada29b18c55c0b4f6a4ee3c119c22f3f00e291f76c9f
View on Chainz β†—

Height

#339,826

Difficulty

10.129932

Transactions

2

Size

359 B

Version

2

Bits

0a214333

Nonce

269,062

Timestamp

1/2/2014, 9:02:13 AM

Confirmations

6,455,726

Mined by

⛏️ jAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

d3d05bc9e59d9fe8cd97496744c29e24bf1cfa335ab0c5487f3a8ab3d514288e
Transactions (2)
Coinbase93dbcbd8eeb9ec…e7af63418dd9e5
1 in β†’ 1 out9.7400 XPM110 B
AeKNrjNj…1NEq95Ta
3ae6af6a5d08df…c36d7f2e782f93
1 in β†’ 1 out9.7000 XPM158 B
AUQWNLX2…FxwsS5kV
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.

3.874 Γ— 10⁹⁢(97-digit number)
38745356668564641054…64910181603092880639
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
3.874 Γ— 10⁹⁢(97-digit number)
38745356668564641054…64910181603092880639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.749 Γ— 10⁹⁢(97-digit number)
77490713337129282109…29820363206185761279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.549 Γ— 10⁹⁷(98-digit number)
15498142667425856421…59640726412371522559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.099 Γ— 10⁹⁷(98-digit number)
30996285334851712843…19281452824743045119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.199 Γ— 10⁹⁷(98-digit number)
61992570669703425687…38562905649486090239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.239 Γ— 10⁹⁸(99-digit number)
12398514133940685137…77125811298972180479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.479 Γ— 10⁹⁸(99-digit number)
24797028267881370274…54251622597944360959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.959 Γ— 10⁹⁸(99-digit number)
49594056535762740549…08503245195888721919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.918 Γ— 10⁹⁸(99-digit number)
99188113071525481099…17006490391777443839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.983 Γ— 10⁹⁹(100-digit number)
19837622614305096219…34012980783554887679
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:57,608,481 XPMΒ·at block #6,795,551 Β· updates every 60s
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