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Block #1,790,048

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/3/2016, 1:45:08 AM Β· Difficulty 10.7707 Β· 5,015,785 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3ef1cf2045634b6f5c0228aff296a9c73a98f2146fcfd4b88c2b57ebd103df66
View on Chainz β†—

Height

#1,790,048

Difficulty

10.770748

Transactions

2

Size

39.85 KB

Version

2

Bits

0ac54fc2

Nonce

2,047,382,212

Timestamp

10/3/2016, 1:45:08 AM

Confirmations

5,015,785

Mined by

⛏️ P2SHAencjyPQxMCxhr5rhgi4i49he3GKVQtGnx

Merkle Root

4c941d79611857062d6f8452a7e521d5c15911c0a4b728ba69be4b508d29c9c1
Transactions (2)
Coinbase912f2a21d62f58…60da039452a2b1
1 in β†’ 1 out9.0200 XPM109 B
AencjyPQ…GKVQtGnx
192ec08e361d31…161df7fe30ce4f
274 in β†’ 2 out62.5100 XPM39.66 KB
AKSAr8SE…P6BxdAe6AM5njGx6…YA3fbDGM
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.

4.047 Γ— 10⁹⁴(95-digit number)
40478826228596420018…16805480800550284159
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
4.047 Γ— 10⁹⁴(95-digit number)
40478826228596420018…16805480800550284159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.095 Γ— 10⁹⁴(95-digit number)
80957652457192840036…33610961601100568319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.619 Γ— 10⁹⁡(96-digit number)
16191530491438568007…67221923202201136639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.238 Γ— 10⁹⁡(96-digit number)
32383060982877136014…34443846404402273279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.476 Γ— 10⁹⁡(96-digit number)
64766121965754272028…68887692808804546559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.295 Γ— 10⁹⁢(97-digit number)
12953224393150854405…37775385617609093119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.590 Γ— 10⁹⁢(97-digit number)
25906448786301708811…75550771235218186239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.181 Γ— 10⁹⁢(97-digit number)
51812897572603417623…51101542470436372479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.036 Γ— 10⁹⁷(98-digit number)
10362579514520683524…02203084940872744959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.072 Γ— 10⁹⁷(98-digit number)
20725159029041367049…04406169881745489919
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:57,690,751 XPMΒ·at block #6,805,832 Β· updates every 60s
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