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Block #2,193,536

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/5/2017, 1:44:28 AM Β· Difficulty 10.9527 Β· 4,633,086 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
56306c517f3a07fa8d40f8d131bf811e15b6702f4e0c9983e63a214bc28c9998
View on Chainz β†—

Height

#2,193,536

Difficulty

10.952661

Transactions

2

Size

573 B

Version

2

Bits

0af3e192

Nonce

748,911,044

Timestamp

7/5/2017, 1:44:28 AM

Confirmations

4,633,086

Mined by

⛏️ P2SHAQ4fqGEnUQUFeR9aRKMQLfuLkr3gHQkG57

Merkle Root

b0f07aed4a027b97b7018db4f416783a42975a3cdf7d87fff4f275c9fc535a8f
Transactions (2)
Coinbase111b14a40b7f38…7a612e6ed6a0f2
1 in β†’ 1 out8.3300 XPM110 B
AQ4fqGEn…3gHQkG57
c4ba408ba4a895…35348e783e2924
2 in β†’ 2 out1308.8262 XPM373 B
AdLv38Pf…k1z3e6DcAa69J2F4…QgtJm3Ps
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.

9.842 Γ— 10⁹⁴(95-digit number)
98422185328839804588…75133292915039003201
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
9.842 Γ— 10⁹⁴(95-digit number)
98422185328839804588…75133292915039003201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.968 Γ— 10⁹⁡(96-digit number)
19684437065767960917…50266585830078006401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.936 Γ— 10⁹⁡(96-digit number)
39368874131535921835…00533171660156012801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.873 Γ— 10⁹⁡(96-digit number)
78737748263071843671…01066343320312025601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.574 Γ— 10⁹⁢(97-digit number)
15747549652614368734…02132686640624051201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.149 Γ— 10⁹⁢(97-digit number)
31495099305228737468…04265373281248102401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.299 Γ— 10⁹⁢(97-digit number)
62990198610457474936…08530746562496204801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.259 Γ— 10⁹⁷(98-digit number)
12598039722091494987…17061493124992409601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.519 Γ— 10⁹⁷(98-digit number)
25196079444182989974…34122986249984819201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.039 Γ— 10⁹⁷(98-digit number)
50392158888365979949…68245972499969638401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.007 Γ— 10⁹⁸(99-digit number)
10078431777673195989…36491944999939276801
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:57,857,129 XPMΒ·at block #6,826,621 Β· updates every 60s
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