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Block #2,642,574

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/1/2018, 7:02:33 PM Β· Difficulty 11.6571 Β· 4,189,804 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1f21337c91e806075de3cf7850cc198b60da4b4f0cf07cb281452f73348f09b7
View on Chainz β†—

Height

#2,642,574

Difficulty

11.657105

Transactions

2

Size

723 B

Version

2

Bits

0ba8380c

Nonce

20,923,184

Timestamp

5/1/2018, 7:02:33 PM

Confirmations

4,189,804

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

84e8ea3bc02667c764900de3440a4a55430a76cd244f1948f82d8b8b568148f2
Transactions (2)
Coinbase1a3571f8ef5e49…b9e4cbec2165c5
1 in β†’ 1 out7.3600 XPM110 B
Adqah8zh…1WwoHJ9t
9e34e42400775d…366496885e26e4
3 in β†’ 2 out2.2026 XPM523 B
AVhXa3fj…Y6pzurwkAPtsn56P…gGnvo6UT
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.

2.201 Γ— 10⁹⁴(95-digit number)
22015736710502977327…89932510431353109761
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
2.201 Γ— 10⁹⁴(95-digit number)
22015736710502977327…89932510431353109761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.403 Γ— 10⁹⁴(95-digit number)
44031473421005954654…79865020862706219521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.806 Γ— 10⁹⁴(95-digit number)
88062946842011909309…59730041725412439041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.761 Γ— 10⁹⁡(96-digit number)
17612589368402381861…19460083450824878081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.522 Γ— 10⁹⁡(96-digit number)
35225178736804763723…38920166901649756161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.045 Γ— 10⁹⁡(96-digit number)
70450357473609527447…77840333803299512321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.409 Γ— 10⁹⁢(97-digit number)
14090071494721905489…55680667606599024641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.818 Γ— 10⁹⁢(97-digit number)
28180142989443810978…11361335213198049281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.636 Γ— 10⁹⁢(97-digit number)
56360285978887621957…22722670426396098561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.127 Γ— 10⁹⁷(98-digit number)
11272057195777524391…45445340852792197121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.254 Γ— 10⁹⁷(98-digit number)
22544114391555048783…90890681705584394241
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
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