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Block #1,127,244

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/26/2015, 11:24:25 AM Β· Difficulty 10.9246 Β· 5,676,269 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0113a581c696635cec76958c36ef10dcde37bc0486a5fd97f4e13a5920c426d4
View on Chainz β†—

Height

#1,127,244

Difficulty

10.924649

Transactions

2

Size

87.27 KB

Version

2

Bits

0aecb5cf

Nonce

1,690,196,617

Timestamp

6/26/2015, 11:24:25 AM

Confirmations

5,676,269

Mined by

⛏️ P2SHAaMijEFcYD8wxUszTo25BS1NVMvE5uUUgk

Merkle Root

1377ccf8abc595e8d0fe198b8fc6576ac1a3cdd6a01d2885e3614964e6453173
Transactions (2)
Coinbased0bffd8fe763ba…0ddfb39500e861
1 in β†’ 1 out9.2700 XPM109 B
AaMijEFc…vE5uUUgk
9d8e3a8922d9ca…7e6c377d21c6cc
602 in β†’ 2 out1100.0100 XPM87.08 KB
AYKArr5V…V9VqiqCZAN5qL9Pj…6ZDbV969
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.

2.130 Γ— 10⁹⁴(95-digit number)
21308128546687869144…97957238841587320061
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
2.130 Γ— 10⁹⁴(95-digit number)
21308128546687869144…97957238841587320061
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.261 Γ— 10⁹⁴(95-digit number)
42616257093375738289…95914477683174640121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.523 Γ— 10⁹⁴(95-digit number)
85232514186751476578…91828955366349280241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.704 Γ— 10⁹⁡(96-digit number)
17046502837350295315…83657910732698560481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.409 Γ— 10⁹⁡(96-digit number)
34093005674700590631…67315821465397120961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.818 Γ— 10⁹⁡(96-digit number)
68186011349401181262…34631642930794241921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.363 Γ— 10⁹⁢(97-digit number)
13637202269880236252…69263285861588483841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.727 Γ— 10⁹⁢(97-digit number)
27274404539760472504…38526571723176967681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.454 Γ— 10⁹⁢(97-digit number)
54548809079520945009…77053143446353935361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.090 Γ— 10⁹⁷(98-digit number)
10909761815904189001…54106286892707870721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.181 Γ— 10⁹⁷(98-digit number)
21819523631808378003…08212573785415741441
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:57,672,129 XPMΒ·at block #6,803,512 Β· updates every 60s
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