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Block #2,636,694

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/29/2018, 4:32:46 PM Β· Difficulty 11.3960 Β· 4,194,743 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
77e7262644b2f6ecbd05a4583caf246167fd97a5d68bc6888dc6a30634abd486
View on Chainz β†—

Height

#2,636,694

Difficulty

11.395998

Transactions

1

Size

199 B

Version

2

Bits

0b65601c

Nonce

824,829,952

Timestamp

4/29/2018, 4:32:46 PM

Confirmations

4,194,743

Mined by

⛏️ P2SHATBVURY6sVdeA3XNYsVwc7EQ47qm81iWPJ

Merkle Root

91959b574642a46501366a3fa7b687858def70183e3a6e2921bb101d4a3d9da2
Transactions (1)
Coinbase91959b574642a4…bb101d4a3d9da2
1 in β†’ 1 out7.6900 XPM110 B
ATBVURY6…qm81iWPJ
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.

1.186 Γ— 10⁹²(93-digit number)
11860239502824451117…82934366135658134981
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
1.186 Γ— 10⁹²(93-digit number)
11860239502824451117…82934366135658134981
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.372 Γ— 10⁹²(93-digit number)
23720479005648902234…65868732271316269961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.744 Γ— 10⁹²(93-digit number)
47440958011297804468…31737464542632539921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.488 Γ— 10⁹²(93-digit number)
94881916022595608936…63474929085265079841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.897 Γ— 10⁹³(94-digit number)
18976383204519121787…26949858170530159681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.795 Γ— 10⁹³(94-digit number)
37952766409038243574…53899716341060319361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.590 Γ— 10⁹³(94-digit number)
75905532818076487149…07799432682120638721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.518 Γ— 10⁹⁴(95-digit number)
15181106563615297429…15598865364241277441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.036 Γ— 10⁹⁴(95-digit number)
30362213127230594859…31197730728482554881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.072 Γ— 10⁹⁴(95-digit number)
60724426254461189719…62395461456965109761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.214 Γ— 10⁹⁡(96-digit number)
12144885250892237943…24790922913930219521
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:57,895,659 XPMΒ·at block #6,831,436 Β· updates every 60s
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