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Block #2,634,928

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/29/2018, 1:52:36 AM Β· Difficulty 11.2798 Β· 4,204,450 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bc9d71496920b3a597e7c5863d31f8fdb346661fd96dca6c4f82b64024aef5ef
View on Chainz β†—

Height

#2,634,928

Difficulty

11.279843

Transactions

1

Size

201 B

Version

2

Bits

0b47a3cd

Nonce

525,917,680

Timestamp

4/29/2018, 1:52:36 AM

Confirmations

4,204,450

Mined by

⛏️ P2SHAMZ1Xd4cAKryAZhfGA5VoaKEGyXGjnmV75

Merkle Root

f4aebac85bb40b78d8a5acdd66ea0beaa030f05733dcb9a1c559811b48ea4bcc
Transactions (1)
Coinbasef4aebac85bb40b…59811b48ea4bcc
1 in β†’ 1 out7.8500 XPM110 B
AMZ1Xd4c…XGjnmV75
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.

1.023 Γ— 10⁹⁸(99-digit number)
10230099813703253246…19718819322141900801
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
1.023 Γ— 10⁹⁸(99-digit number)
10230099813703253246…19718819322141900801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.046 Γ— 10⁹⁸(99-digit number)
20460199627406506492…39437638644283801601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.092 Γ— 10⁹⁸(99-digit number)
40920399254813012985…78875277288567603201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.184 Γ— 10⁹⁸(99-digit number)
81840798509626025971…57750554577135206401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.636 Γ— 10⁹⁹(100-digit number)
16368159701925205194…15501109154270412801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.273 Γ— 10⁹⁹(100-digit number)
32736319403850410388…31002218308540825601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.547 Γ— 10⁹⁹(100-digit number)
65472638807700820777…62004436617081651201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.309 Γ— 10¹⁰⁰(101-digit number)
13094527761540164155…24008873234163302401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.618 Γ— 10¹⁰⁰(101-digit number)
26189055523080328310…48017746468326604801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.237 Γ— 10¹⁰⁰(101-digit number)
52378111046160656621…96035492936653209601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.047 Γ— 10¹⁰¹(102-digit number)
10475622209232131324…92070985873306419201
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:57,959,307 XPMΒ·at block #6,839,377 Β· updates every 60s
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