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Block #1,432,918

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/28/2016, 1:48:02 PM Β· Difficulty 10.7914 Β· 5,407,844 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4a4f400f9437667eff2c259ebf7085f1afba841465723529129c0515a1de1532
View on Chainz β†—

Height

#1,432,918

Difficulty

10.791378

Transactions

2

Size

575 B

Version

2

Bits

0aca97c6

Nonce

813,289,699

Timestamp

1/28/2016, 1:48:02 PM

Confirmations

5,407,844

Mined by

⛏️ P2SHAT54rxcqyinwwqJPk2e5RHjG6U2KFYnFBa

Merkle Root

b20c724ae36616b4f9dffd61ed1dd7ac0adeb8938be5c7fed8be5d1ea0c48adb
Transactions (2)
Coinbase53d732e8513c8d…e45e7cfa020374
1 in β†’ 1 out8.5800 XPM110 B
AT54rxcq…2KFYnFBa
d42c25e3438c62…6e895bc18c95c9
2 in β†’ 2 out2.0200 XPM376 B
AbbDhji6…WASSsNA3Adk3v3sS…VzP4S9Bj
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.

1.070 Γ— 10⁹²(93-digit number)
10700148732793724765…86223105015870533751
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
1.070 Γ— 10⁹²(93-digit number)
10700148732793724765…86223105015870533751
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.140 Γ— 10⁹²(93-digit number)
21400297465587449531…72446210031741067501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.280 Γ— 10⁹²(93-digit number)
42800594931174899063…44892420063482135001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.560 Γ— 10⁹²(93-digit number)
85601189862349798126…89784840126964270001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.712 Γ— 10⁹³(94-digit number)
17120237972469959625…79569680253928540001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.424 Γ— 10⁹³(94-digit number)
34240475944939919250…59139360507857080001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.848 Γ— 10⁹³(94-digit number)
68480951889879838501…18278721015714160001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.369 Γ— 10⁹⁴(95-digit number)
13696190377975967700…36557442031428320001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.739 Γ— 10⁹⁴(95-digit number)
27392380755951935400…73114884062856640001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.478 Γ— 10⁹⁴(95-digit number)
54784761511903870801…46229768125713280001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.095 Γ— 10⁹⁡(96-digit number)
10956952302380774160…92459536251426560001
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:57,970,438 XPMΒ·at block #6,840,761 Β· updates every 60s
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