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Block #3,259,021

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/8/2019, 8:35:10 PM Β· Difficulty 10.9960 Β· 3,545,173 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ea03e550d3a94733f1e89dff54b6a14bc65dc78c84aaddb17caba89643c3d1fa
View on Chainz β†—

Height

#3,259,021

Difficulty

10.995969

Transactions

2

Size

3.89 KB

Version

2

Bits

0afef7d0

Nonce

378,121,984

Timestamp

7/8/2019, 8:35:10 PM

Confirmations

3,545,173

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

b20f87d5b7ac201c279146ca2fadd9bea20140e69e954e08d04587a382d2eb2a
Transactions (2)
Coinbase798890a6d0f79b…9d7dba9a8af203
1 in β†’ 1 out8.3100 XPM110 B
ASiq2qtK…VMhmk7yL
5fae4b20c88275…79d3b26349556b
25 in β†’ 2 out4033.0650 XPM3.69 KB
AGqacyes…C75xf6F6AWbxGWyF…SN5UHtT2
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.

9.594 Γ— 10⁹⁴(95-digit number)
95946762445189368114…04885345321437064321
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
9.594 Γ— 10⁹⁴(95-digit number)
95946762445189368114…04885345321437064321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.918 Γ— 10⁹⁡(96-digit number)
19189352489037873622…09770690642874128641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.837 Γ— 10⁹⁡(96-digit number)
38378704978075747245…19541381285748257281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.675 Γ— 10⁹⁡(96-digit number)
76757409956151494491…39082762571496514561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.535 Γ— 10⁹⁢(97-digit number)
15351481991230298898…78165525142993029121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.070 Γ— 10⁹⁢(97-digit number)
30702963982460597796…56331050285986058241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.140 Γ— 10⁹⁢(97-digit number)
61405927964921195593…12662100571972116481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.228 Γ— 10⁹⁷(98-digit number)
12281185592984239118…25324201143944232961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.456 Γ— 10⁹⁷(98-digit number)
24562371185968478237…50648402287888465921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.912 Γ— 10⁹⁷(98-digit number)
49124742371936956474…01296804575776931841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.824 Γ— 10⁹⁷(98-digit number)
98249484743873912949…02593609151553863681
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:57,677,606 XPMΒ·at block #6,804,193 Β· updates every 60s
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