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Block #2,670,351

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/20/2018, 7:52:51 PM Β· Difficulty 11.6821 Β· 4,169,832 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6bd72cd4e34f0086e507da2fd417f851e64d48243f7502094568f5a802ee2f61
View on Chainz β†—

Height

#2,670,351

Difficulty

11.682106

Transactions

2

Size

724 B

Version

2

Bits

0bae9e87

Nonce

577,428,567

Timestamp

5/20/2018, 7:52:51 PM

Confirmations

4,169,832

Mined by

⛏️ P2SHAS4f9H9K9y99BHVWwMrdE7SYuwDEFSfgUx

Merkle Root

9641bd93b8bbf52f8cf0feabc4a258e710c545a597308133809fca2b944058f8
Transactions (2)
Coinbase2afe692a31f773…864d43a487ca6a
1 in β†’ 1 out7.3300 XPM110 B
AS4f9H9K…DEFSfgUx
8c48c1ba1c502b…83a7e562f5b63d
3 in β†’ 2 out208.3668 XPM523 B
ATUjGy4S…iE7YeL4RAcmGP8Sm…3iy8uLMx
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.

1.517 Γ— 10⁹⁢(97-digit number)
15174936310002305294…80965425068965253761
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
1.517 Γ— 10⁹⁢(97-digit number)
15174936310002305294…80965425068965253761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.034 Γ— 10⁹⁢(97-digit number)
30349872620004610589…61930850137930507521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.069 Γ— 10⁹⁢(97-digit number)
60699745240009221179…23861700275861015041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.213 Γ— 10⁹⁷(98-digit number)
12139949048001844235…47723400551722030081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.427 Γ— 10⁹⁷(98-digit number)
24279898096003688471…95446801103444060161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.855 Γ— 10⁹⁷(98-digit number)
48559796192007376943…90893602206888120321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.711 Γ— 10⁹⁷(98-digit number)
97119592384014753886…81787204413776240641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.942 Γ— 10⁹⁸(99-digit number)
19423918476802950777…63574408827552481281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.884 Γ— 10⁹⁸(99-digit number)
38847836953605901554…27148817655104962561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.769 Γ— 10⁹⁸(99-digit number)
77695673907211803109…54297635310209925121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.553 Γ— 10⁹⁹(100-digit number)
15539134781442360621…08595270620419850241
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:57,965,787 XPMΒ·at block #6,840,182 Β· updates every 60s
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