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Block #3,048,996

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/11/2019, 11:41:42 PM Β· Difficulty 10.9961 Β· 3,787,967 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8bbf5c0287199724041b4c5806a3bce346c12dbf09d414343bd1c578766ac37c
View on Chainz β†—

Height

#3,048,996

Difficulty

10.996080

Transactions

2

Size

573 B

Version

2

Bits

0afeff21

Nonce

807,172,621

Timestamp

2/11/2019, 11:41:42 PM

Confirmations

3,787,967

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

5ae3402a1947de1649ec17182eb22f383e42c748d4a9e8718373b6c657d1a9ba
Transactions (2)
Coinbase9ded1ac17ee770…f1cab700838e86
1 in β†’ 1 out8.2700 XPM110 B
AbXwmGxD…4XXYP765
e2d6d9900ebb73…bfb59e514b82d6
2 in β†’ 2 out531.3075 XPM373 B
Aap4Sp1G…zvjmzSjUAeTHTL7A…vT1872bk
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.

4.571 Γ— 10⁹⁴(95-digit number)
45716975276809833959…54995693514959919081
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
4.571 Γ— 10⁹⁴(95-digit number)
45716975276809833959…54995693514959919081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.143 Γ— 10⁹⁴(95-digit number)
91433950553619667919…09991387029919838161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.828 Γ— 10⁹⁡(96-digit number)
18286790110723933583…19982774059839676321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.657 Γ— 10⁹⁡(96-digit number)
36573580221447867167…39965548119679352641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.314 Γ— 10⁹⁡(96-digit number)
73147160442895734335…79931096239358705281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.462 Γ— 10⁹⁢(97-digit number)
14629432088579146867…59862192478717410561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.925 Γ— 10⁹⁢(97-digit number)
29258864177158293734…19724384957434821121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.851 Γ— 10⁹⁢(97-digit number)
58517728354316587468…39448769914869642241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.170 Γ— 10⁹⁷(98-digit number)
11703545670863317493…78897539829739284481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.340 Γ— 10⁹⁷(98-digit number)
23407091341726634987…57795079659478568961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.681 Γ— 10⁹⁷(98-digit number)
46814182683453269974…15590159318957137921
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:57,940,003 XPMΒ·at block #6,836,962 Β· updates every 60s
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