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Block #2,635,811

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/29/2018, 9:00:41 AM Β· Difficulty 11.3421 Β· 4,176,878 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f4c58cb0967f04ca9d372c611961180a61f482fed3a4f79b59b478e496e4d1fb
View on Chainz β†—

Height

#2,635,811

Difficulty

11.342083

Transactions

2

Size

428 B

Version

2

Bits

0b5792c0

Nonce

954,818,775

Timestamp

4/29/2018, 9:00:41 AM

Confirmations

4,176,878

Mined by

⛏️ P2SHAQad2iymUt1T1cbJ3oSPLZ7rp9zNHc1aey

Merkle Root

e7d9bda209a77febbb8d5cc4f152ea31536a918244ec35e6066f3d5841808623
Transactions (2)
Coinbase27c125035b573e…71b183de9ef5af
1 in β†’ 1 out7.7700 XPM110 B
AQad2iym…zNHc1aey
b7ac508c222896…9c05a43aa6365b
1 in β†’ 2 out13411.9800 XPM227 B
AbQ7UqSm…6zbB3ceNAaEfFKoy…w6PNMxom
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.

5.947 Γ— 10⁹⁢(97-digit number)
59473044793866461566…61244993156119475201
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
5.947 Γ— 10⁹⁢(97-digit number)
59473044793866461566…61244993156119475201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.189 Γ— 10⁹⁷(98-digit number)
11894608958773292313…22489986312238950401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.378 Γ— 10⁹⁷(98-digit number)
23789217917546584626…44979972624477900801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.757 Γ— 10⁹⁷(98-digit number)
47578435835093169253…89959945248955801601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.515 Γ— 10⁹⁷(98-digit number)
95156871670186338507…79919890497911603201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.903 Γ— 10⁹⁸(99-digit number)
19031374334037267701…59839780995823206401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.806 Γ— 10⁹⁸(99-digit number)
38062748668074535402…19679561991646412801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.612 Γ— 10⁹⁸(99-digit number)
76125497336149070805…39359123983292825601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.522 Γ— 10⁹⁹(100-digit number)
15225099467229814161…78718247966585651201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.045 Γ— 10⁹⁹(100-digit number)
30450198934459628322…57436495933171302401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.090 Γ— 10⁹⁹(100-digit number)
60900397868919256644…14872991866342604801
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,745,547 XPMΒ·at block #6,812,688 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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