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Block #1,740,141

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/30/2016, 1:40:04 AM Β· Difficulty 10.7218 Β· 5,104,689 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c731e87609f5db2f54342d35f8fe54ccd62b1ad0329cc33d19e44653c465802e
View on Chainz β†—

Height

#1,740,141

Difficulty

10.721833

Transactions

1

Size

242 B

Version

2

Bits

0ab8ca11

Nonce

1,086,161,048

Timestamp

8/30/2016, 1:40:04 AM

Confirmations

5,104,689

Mined by

⛏️ P2SHAGkY5Euz5mzpuyGoaReCtspzag5TxsxHeG

Merkle Root

de42d991012291544d5054e8585f37c95b8d7647495565efe9af4154ce19390d
Transactions (1)
Coinbasede42d991012291…af4154ce19390d
1 in β†’ 2 out8.6900 XPM152 B
AGkY5Euz…5TxsxHeGALPu3s2c…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.

6.200 Γ— 10⁹⁴(95-digit number)
62002078457807437272…75627756168699840719
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
6.200 Γ— 10⁹⁴(95-digit number)
62002078457807437272…75627756168699840719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.240 Γ— 10⁹⁡(96-digit number)
12400415691561487454…51255512337399681439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.480 Γ— 10⁹⁡(96-digit number)
24800831383122974908…02511024674799362879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.960 Γ— 10⁹⁡(96-digit number)
49601662766245949817…05022049349598725759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.920 Γ— 10⁹⁡(96-digit number)
99203325532491899635…10044098699197451519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.984 Γ— 10⁹⁢(97-digit number)
19840665106498379927…20088197398394903039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.968 Γ— 10⁹⁢(97-digit number)
39681330212996759854…40176394796789806079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.936 Γ— 10⁹⁢(97-digit number)
79362660425993519708…80352789593579612159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.587 Γ— 10⁹⁷(98-digit number)
15872532085198703941…60705579187159224319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.174 Γ— 10⁹⁷(98-digit number)
31745064170397407883…21411158374318448639
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:58,003,049 XPMΒ·at block #6,844,829 Β· updates every 60s
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