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Block #1,611,520

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/2/2016, 9:57:55 PM Β· Difficulty 10.6056 Β· 5,231,463 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
260123f412f0837d15df5daf5c5b7d158b0fbbff4517679cea026c840bb29378
View on Chainz β†—

Height

#1,611,520

Difficulty

10.605578

Transactions

1

Size

200 B

Version

2

Bits

0a9b0731

Nonce

1,483,845,199

Timestamp

6/2/2016, 9:57:55 PM

Confirmations

5,231,463

Mined by

⛏️ P2SHAR4KiV5EChgjyvd6YP1tWMWv6vJNULZiWL

Merkle Root

478a006cc03218c5da53cd6638e836d8032cbde5b7356fac463c8717d3a561ee
Transactions (1)
Coinbase478a006cc03218…3c8717d3a561ee
1 in β†’ 1 out8.8800 XPM109 B
AR4KiV5E…JNULZiWL
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.

1.728 Γ— 10⁹⁢(97-digit number)
17286301591749462010…28478483828907074559
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
1.728 Γ— 10⁹⁢(97-digit number)
17286301591749462010…28478483828907074559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.457 Γ— 10⁹⁢(97-digit number)
34572603183498924020…56956967657814149119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.914 Γ— 10⁹⁢(97-digit number)
69145206366997848040…13913935315628298239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.382 Γ— 10⁹⁷(98-digit number)
13829041273399569608…27827870631256596479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.765 Γ— 10⁹⁷(98-digit number)
27658082546799139216…55655741262513192959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.531 Γ— 10⁹⁷(98-digit number)
55316165093598278432…11311482525026385919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.106 Γ— 10⁹⁸(99-digit number)
11063233018719655686…22622965050052771839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.212 Γ— 10⁹⁸(99-digit number)
22126466037439311373…45245930100105543679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.425 Γ— 10⁹⁸(99-digit number)
44252932074878622746…90491860200211087359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.850 Γ— 10⁹⁸(99-digit number)
88505864149757245492…80983720400422174719
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:57,988,218 XPMΒ·at block #6,842,982 Β· updates every 60s
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