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Block #1,691,973

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/28/2016, 12:55:55 AM Β· Difficulty 10.6846 Β· 5,148,733 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b184f009f41244882a917224edcfd678af17c8cc1946d3d02ca6464a56ae37ac
View on Chainz β†—

Height

#1,691,973

Difficulty

10.684635

Transactions

1

Size

200 B

Version

2

Bits

0aaf443f

Nonce

1,767,754,866

Timestamp

7/28/2016, 12:55:55 AM

Confirmations

5,148,733

Mined by

⛏️ P2SHAahAFFCd7RkJBFLc5zHbENCEnvnRyR9biP

Merkle Root

7c81224670af5ee02f65b50f9f77a82b650098b5313b6fba312aee68a6573127
Transactions (1)
Coinbase7c81224670af5e…2aee68a6573127
1 in β†’ 1 out8.7500 XPM110 B
AahAFFCd…nRyR9biP
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.

6.753 Γ— 10⁹⁡(96-digit number)
67537029073858515185…76838545652981136001
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
6.753 Γ— 10⁹⁡(96-digit number)
67537029073858515185…76838545652981136001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.350 Γ— 10⁹⁢(97-digit number)
13507405814771703037…53677091305962272001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.701 Γ— 10⁹⁢(97-digit number)
27014811629543406074…07354182611924544001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.402 Γ— 10⁹⁢(97-digit number)
54029623259086812148…14708365223849088001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.080 Γ— 10⁹⁷(98-digit number)
10805924651817362429…29416730447698176001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.161 Γ— 10⁹⁷(98-digit number)
21611849303634724859…58833460895396352001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.322 Γ— 10⁹⁷(98-digit number)
43223698607269449719…17666921790792704001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.644 Γ— 10⁹⁷(98-digit number)
86447397214538899438…35333843581585408001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.728 Γ— 10⁹⁸(99-digit number)
17289479442907779887…70667687163170816001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.457 Γ— 10⁹⁸(99-digit number)
34578958885815559775…41335374326341632001
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:57,969,989 XPMΒ·at block #6,840,705 Β· updates every 60s
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