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Block #1,678,346

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/18/2016, 11:13:50 AM Β· Difficulty 10.6938 Β· 5,164,286 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
22bb6669bdba2bb53aa2bb6476f7f9b7b13600b92d0eed5d303f8e68729b7624
View on Chainz β†—

Height

#1,678,346

Difficulty

10.693759

Transactions

1

Size

199 B

Version

2

Bits

0ab19a30

Nonce

1,051,994,069

Timestamp

7/18/2016, 11:13:50 AM

Confirmations

5,164,286

Mined by

⛏️ P2SHAJtMibBMgQzT65XNhGrBAVzYTitjLeAA6s

Merkle Root

548f4fa89b42df249a8a68e9f93b0ad3881e4a36b7e3884671466dd242da81c3
Transactions (1)
Coinbase548f4fa89b42df…466dd242da81c3
1 in β†’ 1 out8.7300 XPM109 B
AJtMibBM…tjLeAA6s
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.

2.616 Γ— 10⁹⁴(95-digit number)
26161789418471276358…04832189611013088899
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.616 Γ— 10⁹⁴(95-digit number)
26161789418471276358…04832189611013088899
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.232 Γ— 10⁹⁴(95-digit number)
52323578836942552717…09664379222026177799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.046 Γ— 10⁹⁡(96-digit number)
10464715767388510543…19328758444052355599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.092 Γ— 10⁹⁡(96-digit number)
20929431534777021087…38657516888104711199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.185 Γ— 10⁹⁡(96-digit number)
41858863069554042174…77315033776209422399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.371 Γ— 10⁹⁡(96-digit number)
83717726139108084348…54630067552418844799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.674 Γ— 10⁹⁢(97-digit number)
16743545227821616869…09260135104837689599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.348 Γ— 10⁹⁢(97-digit number)
33487090455643233739…18520270209675379199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.697 Γ— 10⁹⁢(97-digit number)
66974180911286467478…37040540419350758399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.339 Γ— 10⁹⁷(98-digit number)
13394836182257293495…74081080838701516799
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,985,489 XPMΒ·at block #6,842,631 Β· updates every 60s
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