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Block #2,131,314

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/25/2017, 12:41:16 AM Β· Difficulty 10.9101 Β· 4,710,766 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ffb8bb3595cf7cf2d6755ffe4cbc3b9c1b5feb5a1ac49ad75cf20df1bc8c1c48
View on Chainz β†—

Height

#2,131,314

Difficulty

10.910087

Transactions

1

Size

199 B

Version

2

Bits

0ae8fb7c

Nonce

1,617,444,948

Timestamp

5/25/2017, 12:41:16 AM

Confirmations

4,710,766

Mined by

⛏️ P2SHAaxRDH3qjrx3D9Gvhs7VWSsgu6GJAYxXM4

Merkle Root

57d6b8146af8b328e7fa7a116e73ccf75284b1146c9752f073a3121d5df02597
Transactions (1)
Coinbase57d6b8146af8b3…a3121d5df02597
1 in β†’ 1 out8.3900 XPM109 B
AaxRDH3q…GJAYxXM4
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.

3.685 Γ— 10⁹⁡(96-digit number)
36856571723083747703…82544519067075288959
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
3.685 Γ— 10⁹⁡(96-digit number)
36856571723083747703…82544519067075288959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.371 Γ— 10⁹⁡(96-digit number)
73713143446167495407…65089038134150577919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.474 Γ— 10⁹⁢(97-digit number)
14742628689233499081…30178076268301155839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.948 Γ— 10⁹⁢(97-digit number)
29485257378466998163…60356152536602311679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.897 Γ— 10⁹⁢(97-digit number)
58970514756933996326…20712305073204623359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.179 Γ— 10⁹⁷(98-digit number)
11794102951386799265…41424610146409246719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.358 Γ— 10⁹⁷(98-digit number)
23588205902773598530…82849220292818493439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.717 Γ— 10⁹⁷(98-digit number)
47176411805547197060…65698440585636986879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.435 Γ— 10⁹⁷(98-digit number)
94352823611094394121…31396881171273973759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.887 Γ— 10⁹⁸(99-digit number)
18870564722218878824…62793762342547947519
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:57,981,024 XPMΒ·at block #6,842,079 Β· updates every 60s
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