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Block #461,047

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/26/2014, 11:06:20 AM Β· Difficulty 10.4153 Β· 6,363,845 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5fbcf5e201dec42fff2d8c95abd09ab7a75534f44497dd159b2d30e4aa30de32
View on Chainz β†—

Height

#461,047

Difficulty

10.415335

Transactions

1

Size

290 B

Version

2

Bits

0a6a5360

Nonce

137,181

Timestamp

3/26/2014, 11:06:20 AM

Confirmations

6,363,845

Mined by

AMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

4429f06fd0e97cd41a905a19b147fe739f81a0b38cc71b8c92c02dad42dd96ee
Transactions (1)
Coinbase4429f06fd0e97c…c02dad42dd96ee
1 in β†’ 4 out9.2000 XPM199 B
AMVf7Jrg…xd5AVR7CALzzzbUz…2Cb4jSDNAa2Amg89…4rjYrsPZAJno7LX2…vo4wdWtY
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.

6.360 Γ— 10⁹⁢(97-digit number)
63605451960369010766…25932129163477436799
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
6.360 Γ— 10⁹⁢(97-digit number)
63605451960369010766…25932129163477436799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.272 Γ— 10⁹⁷(98-digit number)
12721090392073802153…51864258326954873599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.544 Γ— 10⁹⁷(98-digit number)
25442180784147604306…03728516653909747199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.088 Γ— 10⁹⁷(98-digit number)
50884361568295208612…07457033307819494399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.017 Γ— 10⁹⁸(99-digit number)
10176872313659041722…14914066615638988799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.035 Γ— 10⁹⁸(99-digit number)
20353744627318083445…29828133231277977599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.070 Γ— 10⁹⁸(99-digit number)
40707489254636166890…59656266462555955199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.141 Γ— 10⁹⁸(99-digit number)
81414978509272333780…19312532925111910399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.628 Γ— 10⁹⁹(100-digit number)
16282995701854466756…38625065850223820799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.256 Γ— 10⁹⁹(100-digit number)
32565991403708933512…77250131700447641599
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:57,843,217 XPMΒ·at block #6,824,891 Β· updates every 60s
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