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Block #1,409,473

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/12/2016, 12:30:08 AM Β· Difficulty 10.8063 Β· 5,417,534 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b5249f9d487576a4d4a6a7633c4f68b4c1613137791d76070ec7f960507b20d1
View on Chainz β†—

Height

#1,409,473

Difficulty

10.806270

Transactions

3

Size

653 B

Version

2

Bits

0ace67ba

Nonce

1,520,102,317

Timestamp

1/12/2016, 12:30:08 AM

Confirmations

5,417,534

Mined by

⛏️ P2SHALvU3QTofsNrSVB76zpUDt2mwV6DQSZBjC

Merkle Root

b4898d8912823932eadd5cf1d46e05c970e4edbf59c19447cea3ec721915681a
Transactions (3)
Coinbaseda6252630b224d…2488cad08f7061
1 in β†’ 1 out8.5700 XPM109 B
ALvU3QTo…6DQSZBjC
1c0b981735a06f…41e152aa126fef
1 in β†’ 2 out130176.9490 XPM226 B
AcMpew3F…1yR4JhRaANxZyuP6…i4sW2tBH
560f09af5d108d…7828ae8134e46c
1 in β†’ 2 out129977.9490 XPM227 B
AcMpew3F…1yR4JhRaAT8J9ahX…iAyLuqP9
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.

2.816 Γ— 10⁹⁢(97-digit number)
28166218188999478575…23493085899103979521
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.816 Γ— 10⁹⁢(97-digit number)
28166218188999478575…23493085899103979521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.633 Γ— 10⁹⁢(97-digit number)
56332436377998957151…46986171798207959041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.126 Γ— 10⁹⁷(98-digit number)
11266487275599791430…93972343596415918081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.253 Γ— 10⁹⁷(98-digit number)
22532974551199582860…87944687192831836161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.506 Γ— 10⁹⁷(98-digit number)
45065949102399165721…75889374385663672321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.013 Γ— 10⁹⁷(98-digit number)
90131898204798331442…51778748771327344641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.802 Γ— 10⁹⁸(99-digit number)
18026379640959666288…03557497542654689281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.605 Γ— 10⁹⁸(99-digit number)
36052759281919332577…07114995085309378561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.210 Γ— 10⁹⁸(99-digit number)
72105518563838665154…14229990170618757121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.442 Γ— 10⁹⁹(100-digit number)
14421103712767733030…28459980341237514241
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,860,232 XPMΒ·at block #6,827,006 Β· updates every 60s
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