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Block #2,558,639

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/10/2018, 12:00:05 PM Β· Difficulty 10.9917 Β· 4,275,255 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b28c9bbedc2d62a1e17ff65616987d798b636d1c372c680cd393cfe2dc884357
View on Chainz β†—

Height

#2,558,639

Difficulty

10.991690

Transactions

1

Size

200 B

Version

2

Bits

0afddf6b

Nonce

764,662,972

Timestamp

3/10/2018, 12:00:05 PM

Confirmations

4,275,255

Mined by

⛏️ P2SHAd21tJiCebicXaHRF4e1RZHSGDhi6ZDXmC

Merkle Root

bff4e6dea9be56071ed4bc326a437e18f00a6d630d3857b132ded221f10b3e7a
Transactions (1)
Coinbasebff4e6dea9be56…ded221f10b3e7a
1 in β†’ 1 out8.2600 XPM110 B
Ad21tJiC…hi6ZDXmC
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.

1.199 Γ— 10⁹⁡(96-digit number)
11994745530168902620…36170939134453197441
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
1.199 Γ— 10⁹⁡(96-digit number)
11994745530168902620…36170939134453197441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.398 Γ— 10⁹⁡(96-digit number)
23989491060337805241…72341878268906394881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.797 Γ— 10⁹⁡(96-digit number)
47978982120675610482…44683756537812789761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.595 Γ— 10⁹⁡(96-digit number)
95957964241351220964…89367513075625579521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.919 Γ— 10⁹⁢(97-digit number)
19191592848270244192…78735026151251159041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.838 Γ— 10⁹⁢(97-digit number)
38383185696540488385…57470052302502318081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.676 Γ— 10⁹⁢(97-digit number)
76766371393080976771…14940104605004636161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.535 Γ— 10⁹⁷(98-digit number)
15353274278616195354…29880209210009272321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.070 Γ— 10⁹⁷(98-digit number)
30706548557232390708…59760418420018544641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.141 Γ— 10⁹⁷(98-digit number)
61413097114464781417…19520836840037089281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.228 Γ— 10⁹⁸(99-digit number)
12282619422892956283…39041673680074178561
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:57,915,376 XPMΒ·at block #6,833,893 Β· updates every 60s
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