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Block #2,654,863

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/9/2018, 4:51:18 PM Β· Difficulty 11.7138 Β· 4,186,503 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b3b91dd361e78e1dfaf24a8bd18c63d43535718985a00b9f58acdf4b0d542440
View on Chainz β†—

Height

#2,654,863

Difficulty

11.713767

Transactions

3

Size

13.47 KB

Version

2

Bits

0bb6b973

Nonce

216,672,486

Timestamp

5/9/2018, 4:51:18 PM

Confirmations

4,186,503

Mined by

⛏️ P2SHAUjj7v5WQkKJwEcdqwjwjL493VAS9RHebL

Merkle Root

3e7457454389d334b5e8cf7731428e759e2a1add16713687a60b086c9dd4027e
Transactions (3)
Coinbasec2e7def38c34fc…b5d6bfe0be9e97
1 in β†’ 1 out7.4300 XPM109 B
AUjj7v5W…AS9RHebL
f79119a108d771…070d73aa5f0780
2 in β†’ 2 out594.1515 XPM373 B
APcoW5SM…9J42xLhnAKf74TEF…iNryuktP
66a4d77559242a…921999482711ae
89 in β†’ 1 out355.8600 XPM12.91 KB
AZ3QSf7f…zd1mV8bu
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.

1.151 Γ— 10⁹³(94-digit number)
11513629952163546503…85098900738243731201
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
1.151 Γ— 10⁹³(94-digit number)
11513629952163546503…85098900738243731201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.302 Γ— 10⁹³(94-digit number)
23027259904327093006…70197801476487462401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.605 Γ— 10⁹³(94-digit number)
46054519808654186012…40395602952974924801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.210 Γ— 10⁹³(94-digit number)
92109039617308372024…80791205905949849601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.842 Γ— 10⁹⁴(95-digit number)
18421807923461674404…61582411811899699201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.684 Γ— 10⁹⁴(95-digit number)
36843615846923348809…23164823623799398401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.368 Γ— 10⁹⁴(95-digit number)
73687231693846697619…46329647247598796801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.473 Γ— 10⁹⁡(96-digit number)
14737446338769339523…92659294495197593601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.947 Γ— 10⁹⁡(96-digit number)
29474892677538679047…85318588990395187201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.894 Γ— 10⁹⁡(96-digit number)
58949785355077358095…70637177980790374401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.178 Γ— 10⁹⁢(97-digit number)
11789957071015471619…41274355961580748801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
2.357 Γ— 10⁹⁢(97-digit number)
23579914142030943238…82548711923161497601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,975,297 XPMΒ·at block #6,841,365 Β· updates every 60s
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