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Block #276,687

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/27/2013, 7:08:58 AM Β· Difficulty 9.9639 Β· 6,519,409 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
782abdda9d8de8f22b6c26fa808838d790907aa65fceeb8a414696a797798cdb
View on Chainz β†—

Height

#276,687

Difficulty

9.963857

Transactions

2

Size

1.69 KB

Version

2

Bits

09f6bf5c

Nonce

57,733

Timestamp

11/27/2013, 7:08:58 AM

Confirmations

6,519,409

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

19132eb7b59418005d49cb94fc5b44288becde6225007783d3e3df405616ed47
Transactions (2)
Coinbase49866252754cbe…9f96a1af1efc04
1 in β†’ 1 out10.0800 XPM110 B
AeKNrjNj…1NEq95Ta
2df8e22227d102…a8c8b9d4834ae4
13 in β†’ 1 out228.6700 XPM1.49 KB
AZLdb3eR…Zx5CExCW
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.

4.926 Γ— 10⁹³(94-digit number)
49263614708710446810…37094858114482274041
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
4.926 Γ— 10⁹³(94-digit number)
49263614708710446810…37094858114482274041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.852 Γ— 10⁹³(94-digit number)
98527229417420893621…74189716228964548081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.970 Γ— 10⁹⁴(95-digit number)
19705445883484178724…48379432457929096161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.941 Γ— 10⁹⁴(95-digit number)
39410891766968357448…96758864915858192321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.882 Γ— 10⁹⁴(95-digit number)
78821783533936714897…93517729831716384641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.576 Γ— 10⁹⁡(96-digit number)
15764356706787342979…87035459663432769281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.152 Γ— 10⁹⁡(96-digit number)
31528713413574685958…74070919326865538561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.305 Γ— 10⁹⁡(96-digit number)
63057426827149371917…48141838653731077121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.261 Γ— 10⁹⁢(97-digit number)
12611485365429874383…96283677307462154241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.522 Γ— 10⁹⁢(97-digit number)
25222970730859748767…92567354614924308481
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,612,768 XPMΒ·at block #6,796,095 Β· updates every 60s
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