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Block #1,634,726

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/18/2016, 11:18:17 PM Β· Difficulty 10.6134 Β· 5,190,288 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
42cff7372137a8a83c699451e067a42351b97cfaf6debe0d3a756522f5c631f9
View on Chainz β†—

Height

#1,634,726

Difficulty

10.613360

Transactions

2

Size

1.43 KB

Version

2

Bits

0a9d052b

Nonce

1,091,278,729

Timestamp

6/18/2016, 11:18:17 PM

Confirmations

5,190,288

Mined by

⛏️ P2SHAc3Gbnw74o1a163Wddrp2QxpUcNr9xy1BX

Merkle Root

7de67a418aab842cd58c19b790c04235863fbd9318d7aece8e4d3dc65e9d7fe2
Transactions (2)
Coinbase88f339239ecd4d…262acae1435d09
1 in β†’ 1 out8.8800 XPM109 B
Ac3Gbnw7…Nr9xy1BX
be226d733c1655…313bb992bcabd6
8 in β†’ 2 out8.8552 XPM1.23 KB
AR1eaXi7…iVTtCTVyAGj3D1np…5UmCsLPB
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.

1.223 Γ— 10⁹⁡(96-digit number)
12237181696410182962…63080495898508834561
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
1.223 Γ— 10⁹⁡(96-digit number)
12237181696410182962…63080495898508834561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.447 Γ— 10⁹⁡(96-digit number)
24474363392820365925…26160991797017669121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.894 Γ— 10⁹⁡(96-digit number)
48948726785640731851…52321983594035338241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.789 Γ— 10⁹⁡(96-digit number)
97897453571281463702…04643967188070676481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.957 Γ— 10⁹⁢(97-digit number)
19579490714256292740…09287934376141352961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.915 Γ— 10⁹⁢(97-digit number)
39158981428512585481…18575868752282705921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.831 Γ— 10⁹⁢(97-digit number)
78317962857025170962…37151737504565411841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.566 Γ— 10⁹⁷(98-digit number)
15663592571405034192…74303475009130823681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.132 Γ— 10⁹⁷(98-digit number)
31327185142810068384…48606950018261647361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.265 Γ— 10⁹⁷(98-digit number)
62654370285620136769…97213900036523294721
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:57,844,197 XPMΒ·at block #6,825,013 Β· updates every 60s
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