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Block #2,148,051

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/6/2017, 5:14:56 AM Β· Difficulty 10.8948 Β· 4,693,943 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f118ca6d54cf6c1af3d93aa07f3a7d3a39136162428cc4f339f36f85ff1ceceb
View on Chainz β†—

Height

#2,148,051

Difficulty

10.894791

Transactions

2

Size

425 B

Version

2

Bits

0ae5110e

Nonce

1,531,345,244

Timestamp

6/6/2017, 5:14:56 AM

Confirmations

4,693,943

Mined by

⛏️ P2SHARb6ELd27x6CGnYL1DpyWAFH3xuvgXCyrq

Merkle Root

fcf7847d34455c7b23e3c81791c8671743a3179a5c513246be59a6534fe36e67
Transactions (2)
Coinbase80f006e33a44af…1a4040711a34c7
1 in β†’ 1 out8.4200 XPM109 B
ARb6ELd2…uvgXCyrq
32a9f37b82f8a5…f182cd7df44f38
1 in β†’ 2 out139577.9058 XPM226 B
ALuwGALM…8NGYvPPkAR1S2aua…1akdRUvQ
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.

1.132 Γ— 10⁹⁡(96-digit number)
11322096408447946228…72795396697407640081
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
1.132 Γ— 10⁹⁡(96-digit number)
11322096408447946228…72795396697407640081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.264 Γ— 10⁹⁡(96-digit number)
22644192816895892456…45590793394815280161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.528 Γ— 10⁹⁡(96-digit number)
45288385633791784912…91181586789630560321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.057 Γ— 10⁹⁡(96-digit number)
90576771267583569824…82363173579261120641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.811 Γ— 10⁹⁢(97-digit number)
18115354253516713964…64726347158522241281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.623 Γ— 10⁹⁢(97-digit number)
36230708507033427929…29452694317044482561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.246 Γ— 10⁹⁢(97-digit number)
72461417014066855859…58905388634088965121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.449 Γ— 10⁹⁷(98-digit number)
14492283402813371171…17810777268177930241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.898 Γ— 10⁹⁷(98-digit number)
28984566805626742343…35621554536355860481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.796 Γ— 10⁹⁷(98-digit number)
57969133611253484687…71243109072711720961
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:57,980,340 XPMΒ·at block #6,841,993 Β· updates every 60s
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