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Block #3,505,623

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/8/2020, 6:39:38 PM Β· Difficulty 10.9302 Β· 3,334,498 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
eadf73c8e2685a8ae0650d47ab76bc2d3c862574c9bd3287b44b5372192168ad
View on Chainz β†—

Height

#3,505,623

Difficulty

10.930163

Transactions

1

Size

200 B

Version

2

Bits

0aee1f2b

Nonce

1,430,116,493

Timestamp

1/8/2020, 6:39:38 PM

Confirmations

3,334,498

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

5a9fbc98d36d6daf852a5b0df93adf1e68f46a154036645f4604ab323b1a000e
Transactions (1)
Coinbase5a9fbc98d36d6d…04ab323b1a000e
1 in β†’ 1 out8.3600 XPM110 B
ASiq2qtK…VMhmk7yL
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.

4.084 Γ— 10⁹⁴(95-digit number)
40848544516748428566…84821055659713273441
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
4.084 Γ— 10⁹⁴(95-digit number)
40848544516748428566…84821055659713273441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.169 Γ— 10⁹⁴(95-digit number)
81697089033496857133…69642111319426546881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.633 Γ— 10⁹⁡(96-digit number)
16339417806699371426…39284222638853093761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.267 Γ— 10⁹⁡(96-digit number)
32678835613398742853…78568445277706187521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.535 Γ— 10⁹⁡(96-digit number)
65357671226797485706…57136890555412375041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.307 Γ— 10⁹⁢(97-digit number)
13071534245359497141…14273781110824750081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.614 Γ— 10⁹⁢(97-digit number)
26143068490718994282…28547562221649500161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.228 Γ— 10⁹⁢(97-digit number)
52286136981437988565…57095124443299000321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.045 Γ— 10⁹⁷(98-digit number)
10457227396287597713…14190248886598000641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.091 Γ— 10⁹⁷(98-digit number)
20914454792575195426…28380497773196001281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.182 Γ— 10⁹⁷(98-digit number)
41828909585150390852…56760995546392002561
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,965,280 XPMΒ·at block #6,840,120 Β· updates every 60s
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