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Block #2,680,252

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/27/2018, 2:27:57 PM Β· Difficulty 11.6915 Β· 4,153,694 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0fefcfa635cff2058c852879c15504a8bd5e177b884b27c8b5ccd530c436b570
View on Chainz β†—

Height

#2,680,252

Difficulty

11.691503

Transactions

1

Size

199 B

Version

2

Bits

0bb10655

Nonce

2,041,856,933

Timestamp

5/27/2018, 2:27:57 PM

Confirmations

4,153,694

Mined by

⛏️ P2SHAZxv25eDjCxKWSCHFAA3gW77o1QEDMK4CF

Merkle Root

7d550048ecc1e7577283b2c138491fe563e2172e310328e877f940747aa7e4a2
Transactions (1)
Coinbase7d550048ecc1e7…f940747aa7e4a2
1 in β†’ 1 out7.3000 XPM109 B
AZxv25eD…QEDMK4CF
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.

5.013 Γ— 10⁹³(94-digit number)
50137521851318984868…35507171245316955839
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
5.013 Γ— 10⁹³(94-digit number)
50137521851318984868…35507171245316955839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.002 Γ— 10⁹⁴(95-digit number)
10027504370263796973…71014342490633911679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.005 Γ— 10⁹⁴(95-digit number)
20055008740527593947…42028684981267823359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.011 Γ— 10⁹⁴(95-digit number)
40110017481055187894…84057369962535646719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.022 Γ— 10⁹⁴(95-digit number)
80220034962110375789…68114739925071293439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.604 Γ— 10⁹⁡(96-digit number)
16044006992422075157…36229479850142586879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.208 Γ— 10⁹⁡(96-digit number)
32088013984844150315…72458959700285173759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.417 Γ— 10⁹⁡(96-digit number)
64176027969688300631…44917919400570347519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.283 Γ— 10⁹⁢(97-digit number)
12835205593937660126…89835838801140695039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.567 Γ— 10⁹⁢(97-digit number)
25670411187875320252…79671677602281390079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.134 Γ— 10⁹⁢(97-digit number)
51340822375750640505…59343355204562780159
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:57,915,796 XPMΒ·at block #6,833,945 Β· updates every 60s
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