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Block #2,272,833

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/29/2017, 4:18:22 AM Β· Difficulty 10.9543 Β· 4,571,722 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4c1126a480077aa49cd37a25089d13a40f8693b6e82dcb8f8a9bdb3ef32dde8f
View on Chainz β†—

Height

#2,272,833

Difficulty

10.954318

Transactions

1

Size

201 B

Version

2

Bits

0af44e35

Nonce

1,257,379,973

Timestamp

8/29/2017, 4:18:22 AM

Confirmations

4,571,722

Mined by

⛏️ P2SHAYgApjUHkJbX2J1HoJ2ECzb7SB5K61Wbex

Merkle Root

f52aedffe62c8539c27cbcb8dc6262d0bc6bd449c2d66b93fad1c86dc445d782
Transactions (1)
Coinbasef52aedffe62c85…d1c86dc445d782
1 in β†’ 1 out8.3200 XPM110 B
AYgApjUH…5K61Wbex
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.

4.832 Γ— 10⁹⁢(97-digit number)
48329846491718594408…83093324189589642241
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
4.832 Γ— 10⁹⁢(97-digit number)
48329846491718594408…83093324189589642241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.665 Γ— 10⁹⁢(97-digit number)
96659692983437188816…66186648379179284481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.933 Γ— 10⁹⁷(98-digit number)
19331938596687437763…32373296758358568961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.866 Γ— 10⁹⁷(98-digit number)
38663877193374875526…64746593516717137921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.732 Γ— 10⁹⁷(98-digit number)
77327754386749751053…29493187033434275841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.546 Γ— 10⁹⁸(99-digit number)
15465550877349950210…58986374066868551681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.093 Γ— 10⁹⁸(99-digit number)
30931101754699900421…17972748133737103361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.186 Γ— 10⁹⁸(99-digit number)
61862203509399800842…35945496267474206721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.237 Γ— 10⁹⁹(100-digit number)
12372440701879960168…71890992534948413441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.474 Γ— 10⁹⁹(100-digit number)
24744881403759920337…43781985069896826881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.948 Γ— 10⁹⁹(100-digit number)
49489762807519840674…87563970139793653761
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:58,000,843 XPMΒ·at block #6,844,554 Β· updates every 60s
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