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Block #318,956

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/18/2013, 5:18:04 PM Β· Difficulty 10.1625 Β· 6,505,900 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a33ba0d6678ec1908772b61f199f9f126eeb1a251ded3ad0ef99d86166cc014c
View on Chainz β†—

Height

#318,956

Difficulty

10.162457

Transactions

1

Size

207 B

Version

2

Bits

0a2996c9

Nonce

36,915

Timestamp

12/18/2013, 5:18:04 PM

Confirmations

6,505,900

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

072b6832b716906c12f2a9af04e8f73af17ea156e8dd04c77d3ec94ae367ab2e
Transactions (1)
Coinbase072b6832b71690…3ec94ae367ab2e
1 in β†’ 1 out9.6700 XPM116 B
AbwWkWZt…kawDhufa
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.

1.124 Γ— 10⁹⁢(97-digit number)
11246435732930749639…37053015225983731199
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.124 Γ— 10⁹⁢(97-digit number)
11246435732930749639…37053015225983731199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.249 Γ— 10⁹⁢(97-digit number)
22492871465861499278…74106030451967462399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.498 Γ— 10⁹⁢(97-digit number)
44985742931722998556…48212060903934924799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.997 Γ— 10⁹⁢(97-digit number)
89971485863445997113…96424121807869849599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.799 Γ— 10⁹⁷(98-digit number)
17994297172689199422…92848243615739699199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.598 Γ— 10⁹⁷(98-digit number)
35988594345378398845…85696487231479398399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.197 Γ— 10⁹⁷(98-digit number)
71977188690756797690…71392974462958796799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.439 Γ— 10⁹⁸(99-digit number)
14395437738151359538…42785948925917593599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.879 Γ— 10⁹⁸(99-digit number)
28790875476302719076…85571897851835187199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.758 Γ— 10⁹⁸(99-digit number)
57581750952605438152…71143795703670374399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,842,931 XPMΒ·at block #6,824,855 Β· updates every 60s
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