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Block #3,046,792

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/10/2019, 9:32:54 AM Β· Difficulty 11.0006 Β· 3,793,969 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a51ef980eeccc3b95b2f9e46a5fbda83d280ffe7b3393db5c4e3ec56b78737e4
View on Chainz β†—

Height

#3,046,792

Difficulty

11.000570

Transactions

2

Size

720 B

Version

2

Bits

0b002561

Nonce

1,005,700,363

Timestamp

2/10/2019, 9:32:54 AM

Confirmations

3,793,969

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

295a1c7eb34fea6ad56dc890f61f5cecc100942f96f5ae0ecca99ba061d33c88
Transactions (2)
Coinbase3cc79f440cf692…d194cf3020bd37
1 in β†’ 1 out8.2600 XPM109 B
AUhjokok…k5m93PZR
d91f746099d70c…41ae68348fa291
3 in β†’ 2 out573.1830 XPM521 B
AJF7BtRy…tfd7vLpzAeTHTL7A…vT1872bk
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.

1.562 Γ— 10⁹⁡(96-digit number)
15628370861958743176…92836957720724298239
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
1.562 Γ— 10⁹⁡(96-digit number)
15628370861958743176…92836957720724298239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.125 Γ— 10⁹⁡(96-digit number)
31256741723917486353…85673915441448596479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.251 Γ— 10⁹⁡(96-digit number)
62513483447834972707…71347830882897192959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.250 Γ— 10⁹⁢(97-digit number)
12502696689566994541…42695661765794385919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.500 Γ— 10⁹⁢(97-digit number)
25005393379133989082…85391323531588771839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.001 Γ— 10⁹⁢(97-digit number)
50010786758267978165…70782647063177543679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.000 Γ— 10⁹⁷(98-digit number)
10002157351653595633…41565294126355087359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.000 Γ— 10⁹⁷(98-digit number)
20004314703307191266…83130588252710174719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.000 Γ— 10⁹⁷(98-digit number)
40008629406614382532…66261176505420349439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.001 Γ— 10⁹⁷(98-digit number)
80017258813228765065…32522353010840698879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.600 Γ— 10⁹⁸(99-digit number)
16003451762645753013…65044706021681397759
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,970,430 XPMΒ·at block #6,840,760 Β· updates every 60s
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