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Block #462,286

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/27/2014, 8:40:29 AM Β· Difficulty 10.4096 Β· 6,368,951 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fc1f2cd86caf0ffb7a18e6c7272384bd827d41bbd31922c76d3a3472d5fe9152
View on Chainz β†—

Height

#462,286

Difficulty

10.409557

Transactions

1

Size

289 B

Version

2

Bits

0a68d8c0

Nonce

629,994

Timestamp

3/27/2014, 8:40:29 AM

Confirmations

6,368,951

Mined by

⛏️ BAMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

7329339038b3fa7cc19f9d7410c1ff0cd23da405a64d0e8eff1d6d2b1fbee5fc
Transactions (1)
Coinbase7329339038b3fa…1d6d2b1fbee5fc
1 in β†’ 4 out9.2100 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.

4.045 Γ— 10⁹⁡(96-digit number)
40454857977535595664…98248250591511627679
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
4.045 Γ— 10⁹⁡(96-digit number)
40454857977535595664…98248250591511627679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.090 Γ— 10⁹⁡(96-digit number)
80909715955071191329…96496501183023255359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.618 Γ— 10⁹⁢(97-digit number)
16181943191014238265…92993002366046510719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.236 Γ— 10⁹⁢(97-digit number)
32363886382028476531…85986004732093021439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.472 Γ— 10⁹⁢(97-digit number)
64727772764056953063…71972009464186042879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.294 Γ— 10⁹⁷(98-digit number)
12945554552811390612…43944018928372085759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.589 Γ— 10⁹⁷(98-digit number)
25891109105622781225…87888037856744171519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.178 Γ— 10⁹⁷(98-digit number)
51782218211245562450…75776075713488343039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.035 Γ— 10⁹⁸(99-digit number)
10356443642249112490…51552151426976686079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.071 Γ— 10⁹⁸(99-digit number)
20712887284498224980…03104302853953372159
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:57,894,045 XPMΒ·at block #6,831,236 Β· updates every 60s
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