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Block #1,679,419

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/19/2016, 3:20:15 AM Β· Difficulty 10.7001 Β· 5,157,215 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8157de5671c43f36d79286c32b33abd30b52b93dd3e2c24015b2388da027475b
View on Chainz β†—

Height

#1,679,419

Difficulty

10.700108

Transactions

1

Size

200 B

Version

2

Bits

0ab33a47

Nonce

279,763,745

Timestamp

7/19/2016, 3:20:15 AM

Confirmations

5,157,215

Mined by

⛏️ P2SHAbgHt8SpLjeCxVvkDAjZTcUqMM4jN8QKev

Merkle Root

544df1e6f8ba0db01955cb8bb62866bb094f7556050f601b84689c3ee6ef7c5f
Transactions (1)
Coinbase544df1e6f8ba0d…689c3ee6ef7c5f
1 in β†’ 1 out8.7200 XPM110 B
AbgHt8Sp…4jN8QKev
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.

3.031 Γ— 10⁹⁡(96-digit number)
30315443849665906588…20012193399819129601
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
3.031 Γ— 10⁹⁡(96-digit number)
30315443849665906588…20012193399819129601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.063 Γ— 10⁹⁡(96-digit number)
60630887699331813176…40024386799638259201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.212 Γ— 10⁹⁢(97-digit number)
12126177539866362635…80048773599276518401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.425 Γ— 10⁹⁢(97-digit number)
24252355079732725270…60097547198553036801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.850 Γ— 10⁹⁢(97-digit number)
48504710159465450541…20195094397106073601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.700 Γ— 10⁹⁢(97-digit number)
97009420318930901082…40390188794212147201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.940 Γ— 10⁹⁷(98-digit number)
19401884063786180216…80780377588424294401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.880 Γ— 10⁹⁷(98-digit number)
38803768127572360433…61560755176848588801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.760 Γ— 10⁹⁷(98-digit number)
77607536255144720866…23121510353697177601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.552 Γ— 10⁹⁸(99-digit number)
15521507251028944173…46243020707394355201
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:57,937,344 XPMΒ·at block #6,836,633 Β· updates every 60s
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