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Block #2,123,648

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/19/2017, 9:46:22 AM Β· Difficulty 10.9172 Β· 4,719,880 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a1a2ed2ccfe692a160ce1fb46e27e5f9f76ca60da2e4f5cdf59eee0c9eaa5bbf
View on Chainz β†—

Height

#2,123,648

Difficulty

10.917175

Transactions

1

Size

242 B

Version

2

Bits

0aeacbf5

Nonce

383,592,425

Timestamp

5/19/2017, 9:46:22 AM

Confirmations

4,719,880

Mined by

⛏️ P2SHAMMJ7Ku9ctFmjCbBPtKsnh34K5ZYGbYo5z

Merkle Root

848e9d1aed859918604df905193685451834f91991ab75fe59dd7c62ac049a4c
Transactions (1)
Coinbase848e9d1aed8599…dd7c62ac049a4c
1 in β†’ 2 out8.3800 XPM152 B
AMMJ7Ku9…ZYGbYo5zAXbk7f7A…Tx7JECPG
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.

9.025 Γ— 10⁹⁴(95-digit number)
90250145137567227600…21980090420692933341
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
9.025 Γ— 10⁹⁴(95-digit number)
90250145137567227600…21980090420692933341
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.805 Γ— 10⁹⁡(96-digit number)
18050029027513445520…43960180841385866681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.610 Γ— 10⁹⁡(96-digit number)
36100058055026891040…87920361682771733361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.220 Γ— 10⁹⁡(96-digit number)
72200116110053782080…75840723365543466721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.444 Γ— 10⁹⁢(97-digit number)
14440023222010756416…51681446731086933441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.888 Γ— 10⁹⁢(97-digit number)
28880046444021512832…03362893462173866881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.776 Γ— 10⁹⁢(97-digit number)
57760092888043025664…06725786924347733761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.155 Γ— 10⁹⁷(98-digit number)
11552018577608605132…13451573848695467521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.310 Γ— 10⁹⁷(98-digit number)
23104037155217210265…26903147697390935041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.620 Γ— 10⁹⁷(98-digit number)
46208074310434420531…53806295394781870081
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,992,601 XPMΒ·at block #6,843,527 Β· updates every 60s
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