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Block #1,368,321

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/13/2015, 8:06:38 PM Β· Difficulty 10.8358 Β· 5,462,916 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
66c733a57364244883dad1a1d2a725e779222cf5587df87be07e9fff948ef834
View on Chainz β†—

Height

#1,368,321

Difficulty

10.835832

Transactions

1

Size

200 B

Version

2

Bits

0ad5f914

Nonce

333,867,407

Timestamp

12/13/2015, 8:06:38 PM

Confirmations

5,462,916

Mined by

⛏️ P2SHAcVaJUT3Umd8FjxNkd8gytbL8sDCiXp9eV

Merkle Root

19079006c936a6314ce7540bbf0acd474b739e2507eceb3fe65c7323925ba53f
Transactions (1)
Coinbase19079006c936a6…5c7323925ba53f
1 in β†’ 1 out8.5000 XPM110 B
AcVaJUT3…DCiXp9eV
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.

7.206 Γ— 10⁹³(94-digit number)
72067695683548181018…08222705373655787521
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
7.206 Γ— 10⁹³(94-digit number)
72067695683548181018…08222705373655787521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.441 Γ— 10⁹⁴(95-digit number)
14413539136709636203…16445410747311575041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.882 Γ— 10⁹⁴(95-digit number)
28827078273419272407…32890821494623150081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.765 Γ— 10⁹⁴(95-digit number)
57654156546838544814…65781642989246300161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.153 Γ— 10⁹⁡(96-digit number)
11530831309367708962…31563285978492600321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.306 Γ— 10⁹⁡(96-digit number)
23061662618735417925…63126571956985200641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.612 Γ— 10⁹⁡(96-digit number)
46123325237470835851…26253143913970401281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.224 Γ— 10⁹⁡(96-digit number)
92246650474941671703…52506287827940802561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.844 Γ— 10⁹⁢(97-digit number)
18449330094988334340…05012575655881605121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.689 Γ— 10⁹⁢(97-digit number)
36898660189976668681…10025151311763210241
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:57,894,045 XPMΒ·at block #6,831,236 Β· updates every 60s
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