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Block #272,378

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/25/2013, 5:42:46 AM Β· Difficulty 9.9527 Β· 6,537,200 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ad0dad22b8ad3c7fffe072a26d28c33a00ea5a283781ba3b8a8deb135531992a
View on Chainz β†—

Height

#272,378

Difficulty

9.952665

Transactions

2

Size

2.11 KB

Version

2

Bits

09f3e1e1

Nonce

19,523

Timestamp

11/25/2013, 5:42:46 AM

Confirmations

6,537,200

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

5b1cd0e32e7d01926f0703860270d634a0cb87c8aa608a8353def0cf0660eb91
Transactions (2)
Coinbased6d89ee8e55f7f…82adfb9786c7f5
1 in β†’ 1 out10.1000 XPM109 B
AeKNrjNj…1NEq95Ta
0fe145da96f388…0be26fe82e027b
13 in β†’ 1 out139.9900 XPM1.92 KB
AFqmCdBa…Ny6V9YGF
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.

1.034 Γ— 10⁹⁡(96-digit number)
10348045894719058638…20930073020082872501
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
1.034 Γ— 10⁹⁡(96-digit number)
10348045894719058638…20930073020082872501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.069 Γ— 10⁹⁡(96-digit number)
20696091789438117277…41860146040165745001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.139 Γ— 10⁹⁡(96-digit number)
41392183578876234555…83720292080331490001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.278 Γ— 10⁹⁡(96-digit number)
82784367157752469111…67440584160662980001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.655 Γ— 10⁹⁢(97-digit number)
16556873431550493822…34881168321325960001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.311 Γ— 10⁹⁢(97-digit number)
33113746863100987644…69762336642651920001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.622 Γ— 10⁹⁢(97-digit number)
66227493726201975289…39524673285303840001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.324 Γ— 10⁹⁷(98-digit number)
13245498745240395057…79049346570607680001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.649 Γ— 10⁹⁷(98-digit number)
26490997490480790115…58098693141215360001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,720,701 XPMΒ·at block #6,809,577 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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