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Block #2,301,280

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/19/2017, 12:49:57 PM Β· Difficulty 10.9292 Β· 4,535,633 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dff032ce2672ccb79aa8bb6317cf68efc051f08ef303d2f90e5e336fd797fc3f
View on Chainz β†—

Height

#2,301,280

Difficulty

10.929162

Transactions

1

Size

200 B

Version

2

Bits

0aeddd92

Nonce

643,713,940

Timestamp

9/19/2017, 12:49:57 PM

Confirmations

4,535,633

Mined by

⛏️ P2SHAGpdAaAr1hncc2TnWaeoQDhM9ap5Fn3ctW

Merkle Root

73f47ce75e9c5110d023475c740e909433ff4e4d20774628aa58a2b8bf240105
Transactions (1)
Coinbase73f47ce75e9c51…58a2b8bf240105
1 in β†’ 1 out8.3600 XPM109 B
AGpdAaAr…p5Fn3ctW
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.

4.881 Γ— 10⁹⁢(97-digit number)
48811852582766274441…41126287153345269759
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
4.881 Γ— 10⁹⁢(97-digit number)
48811852582766274441…41126287153345269759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.762 Γ— 10⁹⁢(97-digit number)
97623705165532548882…82252574306690539519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.952 Γ— 10⁹⁷(98-digit number)
19524741033106509776…64505148613381079039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.904 Γ— 10⁹⁷(98-digit number)
39049482066213019553…29010297226762158079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.809 Γ— 10⁹⁷(98-digit number)
78098964132426039106…58020594453524316159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.561 Γ— 10⁹⁸(99-digit number)
15619792826485207821…16041188907048632319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.123 Γ— 10⁹⁸(99-digit number)
31239585652970415642…32082377814097264639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.247 Γ— 10⁹⁸(99-digit number)
62479171305940831285…64164755628194529279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.249 Γ— 10⁹⁹(100-digit number)
12495834261188166257…28329511256389058559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.499 Γ— 10⁹⁹(100-digit number)
24991668522376332514…56659022512778117119
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:57,939,598 XPMΒ·at block #6,836,912 Β· updates every 60s
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