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Block #1,723,419

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/18/2016, 8:45:01 PM Β· Difficulty 10.6868 Β· 5,093,338 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ee3486ed68d340f2eb4823a82c50d466d4a5dd17b2dcb736540efb8c74f406bf
View on Chainz β†—

Height

#1,723,419

Difficulty

10.686799

Transactions

1

Size

199 B

Version

2

Bits

0aafd217

Nonce

1,246,727,708

Timestamp

8/18/2016, 8:45:01 PM

Confirmations

5,093,338

Mined by

⛏️ P2SHALeT6mxSthUmKDKrJcDk2HuHTBzoJ4jw8X

Merkle Root

20d766951d02b7c99de05a935049f27b41d2863645a4087f9d3ad4286ed7f8a5
Transactions (1)
Coinbase20d766951d02b7…3ad4286ed7f8a5
1 in β†’ 1 out8.7400 XPM109 B
ALeT6mxS…zoJ4jw8X
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.

4.937 Γ— 10⁹⁡(96-digit number)
49378690039403165936…85787466835179179199
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
4.937 Γ— 10⁹⁡(96-digit number)
49378690039403165936…85787466835179179199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.875 Γ— 10⁹⁡(96-digit number)
98757380078806331873…71574933670358358399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.975 Γ— 10⁹⁢(97-digit number)
19751476015761266374…43149867340716716799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.950 Γ— 10⁹⁢(97-digit number)
39502952031522532749…86299734681433433599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.900 Γ— 10⁹⁢(97-digit number)
79005904063045065498…72599469362866867199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.580 Γ— 10⁹⁷(98-digit number)
15801180812609013099…45198938725733734399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.160 Γ— 10⁹⁷(98-digit number)
31602361625218026199…90397877451467468799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.320 Γ— 10⁹⁷(98-digit number)
63204723250436052398…80795754902934937599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.264 Γ— 10⁹⁸(99-digit number)
12640944650087210479…61591509805869875199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.528 Γ— 10⁹⁸(99-digit number)
25281889300174420959…23183019611739750399
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:57,778,087 XPMΒ·at block #6,816,756 Β· updates every 60s
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