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Block #1,885,096

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/8/2016, 9:28:43 PM Β· Difficulty 10.7149 Β· 4,946,022 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
689a46e732e7750ba25504324e33bd4b0c06cf14d8fea37426f66eedd2424a99
View on Chainz β†—

Height

#1,885,096

Difficulty

10.714891

Transactions

1

Size

243 B

Version

2

Bits

0ab70317

Nonce

353,739,043

Timestamp

12/8/2016, 9:28:43 PM

Confirmations

4,946,022

Mined by

⛏️ P2SHAMeY5ZrV7AqtjFwPLjnwr3BDd53veG96Ko

Merkle Root

77b3047124d126cb7b5ad8c0ce4e030b1d7ece5d67b1052c7bdaf8633f108029
Transactions (1)
Coinbase77b3047124d126…daf8633f108029
1 in β†’ 2 out8.7000 XPM152 B
AMeY5ZrV…3veG96KoALPu3s2c…EJXLjVFh
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.

5.348 Γ— 10⁹⁢(97-digit number)
53484199162852943248…16104899509169520641
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
5.348 Γ— 10⁹⁢(97-digit number)
53484199162852943248…16104899509169520641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.069 Γ— 10⁹⁷(98-digit number)
10696839832570588649…32209799018339041281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.139 Γ— 10⁹⁷(98-digit number)
21393679665141177299…64419598036678082561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.278 Γ— 10⁹⁷(98-digit number)
42787359330282354598…28839196073356165121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.557 Γ— 10⁹⁷(98-digit number)
85574718660564709196…57678392146712330241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.711 Γ— 10⁹⁸(99-digit number)
17114943732112941839…15356784293424660481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.422 Γ— 10⁹⁸(99-digit number)
34229887464225883678…30713568586849320961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.845 Γ— 10⁹⁸(99-digit number)
68459774928451767357…61427137173698641921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.369 Γ— 10⁹⁹(100-digit number)
13691954985690353471…22854274347397283841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.738 Γ— 10⁹⁹(100-digit number)
27383909971380706943…45708548694794567681
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:57,893,090 XPMΒ·at block #6,831,117 Β· updates every 60s
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