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Block #2,207,423

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/15/2017, 5:53:26 AM Β· Difficulty 10.9454 Β· 4,637,907 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b8560b3f0cf81f1f4c2c73d8a8a2bb59fa57a53d740417db8323a97eb485bb0d
View on Chainz β†—

Height

#2,207,423

Difficulty

10.945405

Transactions

1

Size

200 B

Version

2

Bits

0af20616

Nonce

1,978,397,505

Timestamp

7/15/2017, 5:53:26 AM

Confirmations

4,637,907

Mined by

⛏️ P2SHAcGaobAUT7f7pwX3iVBFvQ3k4LWtFe7jpF

Merkle Root

7093314c1f108251027ec141b7a9db0ccf1e230b23e3baf83096a2eb630bb156
Transactions (1)
Coinbase7093314c1f1082…96a2eb630bb156
1 in β†’ 1 out8.3300 XPM110 B
AcGaobAU…WtFe7jpF
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.

4.536 Γ— 10⁹⁴(95-digit number)
45362627828029654739…72892732870557425759
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
4.536 Γ— 10⁹⁴(95-digit number)
45362627828029654739…72892732870557425759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.072 Γ— 10⁹⁴(95-digit number)
90725255656059309478…45785465741114851519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.814 Γ— 10⁹⁡(96-digit number)
18145051131211861895…91570931482229703039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.629 Γ— 10⁹⁡(96-digit number)
36290102262423723791…83141862964459406079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.258 Γ— 10⁹⁡(96-digit number)
72580204524847447582…66283725928918812159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.451 Γ— 10⁹⁢(97-digit number)
14516040904969489516…32567451857837624319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.903 Γ— 10⁹⁢(97-digit number)
29032081809938979033…65134903715675248639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.806 Γ— 10⁹⁢(97-digit number)
58064163619877958066…30269807431350497279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.161 Γ— 10⁹⁷(98-digit number)
11612832723975591613…60539614862700994559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.322 Γ— 10⁹⁷(98-digit number)
23225665447951183226…21079229725401989119
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:58,007,080 XPMΒ·at block #6,845,329 Β· updates every 60s
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