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Block #2,639,029

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2018, 12:21:00 PM Β· Difficulty 11.5190 Β· 4,204,974 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
39eb2ab6a92b1f93c4b637819db3af777cfacbab818e4ed0c81ccc372a9cb161
View on Chainz β†—

Height

#2,639,029

Difficulty

11.518968

Transactions

2

Size

391 B

Version

2

Bits

0b84db0f

Nonce

142,882,806

Timestamp

4/30/2018, 12:21:00 PM

Confirmations

4,204,974

Mined by

⛏️ P2SHAJmEju2aqqrSjToQdHuvqYDy1bsmvnqYXf

Merkle Root

3985a9859c5bcf6a87d16f0134ae0e39853ef5ef052c6edcdb3b5daa5e932101
Transactions (2)
Coinbasefe8f0b72155b9c…238cdd48622177
1 in β†’ 1 out7.5300 XPM110 B
AJmEju2a…smvnqYXf
58a8153a6e9daa…a252f0d69c0f9c
1 in β†’ 1 out699.9900 XPM191 B
AZFZtVao…Bge3kTNy
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.

4.048 Γ— 10⁹⁴(95-digit number)
40483312973403943285…53652183653670911041
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
4.048 Γ— 10⁹⁴(95-digit number)
40483312973403943285…53652183653670911041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.096 Γ— 10⁹⁴(95-digit number)
80966625946807886570…07304367307341822081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.619 Γ— 10⁹⁡(96-digit number)
16193325189361577314…14608734614683644161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.238 Γ— 10⁹⁡(96-digit number)
32386650378723154628…29217469229367288321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.477 Γ— 10⁹⁡(96-digit number)
64773300757446309256…58434938458734576641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.295 Γ— 10⁹⁢(97-digit number)
12954660151489261851…16869876917469153281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.590 Γ— 10⁹⁢(97-digit number)
25909320302978523702…33739753834938306561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.181 Γ— 10⁹⁢(97-digit number)
51818640605957047405…67479507669876613121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.036 Γ— 10⁹⁷(98-digit number)
10363728121191409481…34959015339753226241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.072 Γ— 10⁹⁷(98-digit number)
20727456242382818962…69918030679506452481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.145 Γ— 10⁹⁷(98-digit number)
41454912484765637924…39836061359012904961
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:57,996,404 XPMΒ·at block #6,844,002 Β· updates every 60s
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