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Block #1,443,361

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/5/2016, 8:03:04 AM Β· Difficulty 10.7592 Β· 5,401,691 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bc9723211276cb0f218a58e035c2dde7db5ff8040e0ca2ff783e7d7b33f082e1
View on Chainz β†—

Height

#1,443,361

Difficulty

10.759202

Transactions

1

Size

200 B

Version

2

Bits

0ac25b15

Nonce

1,600,066,243

Timestamp

2/5/2016, 8:03:04 AM

Confirmations

5,401,691

Mined by

⛏️ P2SHAaBbY9g4Ztmd35axvQSnu7xUftCACP6ebT

Merkle Root

3e32386501101ec50c6c639ecedce82dce96a71369e780d703cb0efd5dcb636d
Transactions (1)
Coinbase3e32386501101e…cb0efd5dcb636d
1 in β†’ 1 out8.6200 XPM110 B
AaBbY9g4…CACP6ebT
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.

1.479 Γ— 10⁹⁡(96-digit number)
14797646689703879004…74147437782374944799
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
1.479 Γ— 10⁹⁡(96-digit number)
14797646689703879004…74147437782374944799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.959 Γ— 10⁹⁡(96-digit number)
29595293379407758008…48294875564749889599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.919 Γ— 10⁹⁡(96-digit number)
59190586758815516017…96589751129499779199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.183 Γ— 10⁹⁢(97-digit number)
11838117351763103203…93179502258999558399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.367 Γ— 10⁹⁢(97-digit number)
23676234703526206406…86359004517999116799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.735 Γ— 10⁹⁢(97-digit number)
47352469407052412813…72718009035998233599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.470 Γ— 10⁹⁢(97-digit number)
94704938814104825627…45436018071996467199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.894 Γ— 10⁹⁷(98-digit number)
18940987762820965125…90872036143992934399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.788 Γ— 10⁹⁷(98-digit number)
37881975525641930250…81744072287985868799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.576 Γ— 10⁹⁷(98-digit number)
75763951051283860501…63488144575971737599
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:58,004,839 XPMΒ·at block #6,845,051 Β· updates every 60s
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