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Block #1,100,671

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/12/2015, 1:08:51 AM Β· Difficulty 10.7600 Β· 5,697,919 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8bb9dee1d6a089359cccbb5f4e1aff1daa3cce7b154ae97ef3d82890486e8b35
View on Chainz β†—

Height

#1,100,671

Difficulty

10.759967

Transactions

1

Size

200 B

Version

2

Bits

0ac28d39

Nonce

8,974,587

Timestamp

6/12/2015, 1:08:51 AM

Confirmations

5,697,919

Mined by

⛏️ P2SHANCZAhFAbKSZQtiaCEE6qAhDsq4XJ8NSvi

Merkle Root

e21d24bdd557d53c7b4917c8d89e9c94868231549725c2a9caaf06026f3ac1a9
Transactions (1)
Coinbasee21d24bdd557d5…af06026f3ac1a9
1 in β†’ 1 out8.6200 XPM109 B
ANCZAhFA…4XJ8NSvi
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.

8.837 Γ— 10⁹⁡(96-digit number)
88379758931595270073…23977906042511995501
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
8.837 Γ— 10⁹⁡(96-digit number)
88379758931595270073…23977906042511995501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.767 Γ— 10⁹⁢(97-digit number)
17675951786319054014…47955812085023991001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.535 Γ— 10⁹⁢(97-digit number)
35351903572638108029…95911624170047982001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.070 Γ— 10⁹⁢(97-digit number)
70703807145276216058…91823248340095964001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.414 Γ— 10⁹⁷(98-digit number)
14140761429055243211…83646496680191928001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.828 Γ— 10⁹⁷(98-digit number)
28281522858110486423…67292993360383856001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.656 Γ— 10⁹⁷(98-digit number)
56563045716220972846…34585986720767712001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.131 Γ— 10⁹⁸(99-digit number)
11312609143244194569…69171973441535424001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.262 Γ— 10⁹⁸(99-digit number)
22625218286488389138…38343946883070848001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.525 Γ— 10⁹⁸(99-digit number)
45250436572976778277…76687893766141696001
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 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
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,632,733 XPMΒ·at block #6,798,589 Β· updates every 60s
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