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Block #2,634,358

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/28/2018, 8:52:52 PM Β· Difficulty 11.2402 Β· 4,203,673 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c4f6c4052afaacaf573518962a2121de0dbe415580aa14c30e14d96cd14192ef
View on Chainz β†—

Height

#2,634,358

Difficulty

11.240176

Transactions

2

Size

574 B

Version

2

Bits

0b3d7c31

Nonce

13,034,318

Timestamp

4/28/2018, 8:52:52 PM

Confirmations

4,203,673

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

ead063807ba9688e3f0d1e4f4e37ab05cccb16f51c17bd3ac1c3f82c8de9ede1
Transactions (2)
Coinbase1fd0ec48ab8a3d…8c12aff19335cc
1 in β†’ 1 out7.9100 XPM110 B
Adqah8zh…1WwoHJ9t
18aa70fbd68d0d…ee7f0b75838418
2 in β†’ 2 out911.0274 XPM374 B
AaTN4273…RTonuvf3AV2M6eu9…pzEgmZjN
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.

2.184 Γ— 10⁹⁴(95-digit number)
21846239318465738578…80739830246959911201
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
2.184 Γ— 10⁹⁴(95-digit number)
21846239318465738578…80739830246959911201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.369 Γ— 10⁹⁴(95-digit number)
43692478636931477156…61479660493919822401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.738 Γ— 10⁹⁴(95-digit number)
87384957273862954312…22959320987839644801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.747 Γ— 10⁹⁡(96-digit number)
17476991454772590862…45918641975679289601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.495 Γ— 10⁹⁡(96-digit number)
34953982909545181724…91837283951358579201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.990 Γ— 10⁹⁡(96-digit number)
69907965819090363449…83674567902717158401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.398 Γ— 10⁹⁢(97-digit number)
13981593163818072689…67349135805434316801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.796 Γ— 10⁹⁢(97-digit number)
27963186327636145379…34698271610868633601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.592 Γ— 10⁹⁢(97-digit number)
55926372655272290759…69396543221737267201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.118 Γ— 10⁹⁷(98-digit number)
11185274531054458151…38793086443474534401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.237 Γ— 10⁹⁷(98-digit number)
22370549062108916303…77586172886949068801
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:57,948,598 XPMΒ·at block #6,838,030 Β· updates every 60s
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