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Block #804,509

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/9/2014, 9:50:10 PM Β· Difficulty 10.9753 Β· 6,012,932 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5622cc2caa79fb270a5bb14b158589a8a22f7208dc3a695c1b99e63984e5b4b0
View on Chainz β†—

Height

#804,509

Difficulty

10.975262

Transactions

2

Size

434 B

Version

2

Bits

0af9aacb

Nonce

1,709,208,849

Timestamp

11/9/2014, 9:50:10 PM

Confirmations

6,012,932

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

42479d66961c85204428a89b47c369ade4facacb43a23ab9c48455a766485e46
Transactions (2)
Coinbase550c852029ca21…c9c621c32a5334
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
62b8f9bb52c1c1…e85ac39c456aa2
1 in β†’ 2 out2.8196 XPM227 B
Aba6XLEW…giia6sUhAPFMWhi1…fzp599bu
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.

1.626 Γ— 10⁹⁢(97-digit number)
16269377214873150390…24489956624483353601
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
1.626 Γ— 10⁹⁢(97-digit number)
16269377214873150390…24489956624483353601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.253 Γ— 10⁹⁢(97-digit number)
32538754429746300780…48979913248966707201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.507 Γ— 10⁹⁢(97-digit number)
65077508859492601560…97959826497933414401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.301 Γ— 10⁹⁷(98-digit number)
13015501771898520312…95919652995866828801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.603 Γ— 10⁹⁷(98-digit number)
26031003543797040624…91839305991733657601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.206 Γ— 10⁹⁷(98-digit number)
52062007087594081248…83678611983467315201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.041 Γ— 10⁹⁸(99-digit number)
10412401417518816249…67357223966934630401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.082 Γ— 10⁹⁸(99-digit number)
20824802835037632499…34714447933869260801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.164 Γ— 10⁹⁸(99-digit number)
41649605670075264998…69428895867738521601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.329 Γ— 10⁹⁸(99-digit number)
83299211340150529996…38857791735477043201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.665 Γ— 10⁹⁹(100-digit number)
16659842268030105999…77715583470954086401
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:57,783,575 XPMΒ·at block #6,817,440 Β· updates every 60s
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