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Block #8,811

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/10/2013, 6:56:15 PM Β· Difficulty 7.5882 Β· 6,800,549 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
281c9f04dff567ca1496ef34364bb32274daf6ceee9dac756a541fdf4726a16b
View on Chainz β†—

Height

#8,811

Difficulty

7.588167

Transactions

2

Size

1.00 KB

Version

2

Bits

0796921b

Nonce

1,090

Timestamp

7/10/2013, 6:56:15 PM

Confirmations

6,800,549

Mined by

⛏️ P2SHAXdbE92RfouBA7DsZv2tNjt9XT7YBngQfh

Merkle Root

17df09e88ca2ff0f3be5311ca0a94f8a5718386b6080844bbaccb996b1c69273
Transactions (2)
Coinbase28b4521e655f49…58b39c2b115c29
1 in β†’ 1 out17.3500 XPM108 B
AXdbE92R…7YBngQfh
25678f9f46e82f…5d2a98a1da01f7
6 in β†’ 2 out109.8700 XPM828 B
AQWhjfLG…8xZnFKHNAMXWi8Ab…Xf5AUNSo
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.

2.802 Γ— 10⁹³(94-digit number)
28026128394691174414…69862301412247446081
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
2.802 Γ— 10⁹³(94-digit number)
28026128394691174414…69862301412247446081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.605 Γ— 10⁹³(94-digit number)
56052256789382348828…39724602824494892161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.121 Γ— 10⁹⁴(95-digit number)
11210451357876469765…79449205648989784321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.242 Γ— 10⁹⁴(95-digit number)
22420902715752939531…58898411297979568641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.484 Γ— 10⁹⁴(95-digit number)
44841805431505879062…17796822595959137281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.968 Γ— 10⁹⁴(95-digit number)
89683610863011758125…35593645191918274561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.793 Γ— 10⁹⁡(96-digit number)
17936722172602351625…71187290383836549121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.587 Γ— 10⁹⁡(96-digit number)
35873444345204703250…42374580767673098241
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,718,948 XPMΒ·at block #6,809,359 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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