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Block #2,100,190

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/5/2017, 1:02:25 AM Β· Difficulty 10.8553 Β· 4,740,427 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f00d06817bbc2f436828be0bde7ad07f18e02ac58492e07452bc580b93e7aff7
View on Chainz β†—

Height

#2,100,190

Difficulty

10.855348

Transactions

1

Size

200 B

Version

2

Bits

0adaf814

Nonce

306,273,295

Timestamp

5/5/2017, 1:02:25 AM

Confirmations

4,740,427

Mined by

⛏️ P2SHAe6inYvVw7JkNwvcYPqLkWAMAaceHiea5t

Merkle Root

4e866dca634ca189e36ea43f108122311ad7eb6bc25c8f50cd61635e8ee1f758
Transactions (1)
Coinbase4e866dca634ca1…61635e8ee1f758
1 in β†’ 1 out8.4700 XPM110 B
Ae6inYvV…ceHiea5t
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.

7.901 Γ— 10⁹³(94-digit number)
79018803693683633796…95310878490834822699
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
7.901 Γ— 10⁹³(94-digit number)
79018803693683633796…95310878490834822699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.580 Γ— 10⁹⁴(95-digit number)
15803760738736726759…90621756981669645399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.160 Γ— 10⁹⁴(95-digit number)
31607521477473453518…81243513963339290799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.321 Γ— 10⁹⁴(95-digit number)
63215042954946907037…62487027926678581599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.264 Γ— 10⁹⁡(96-digit number)
12643008590989381407…24974055853357163199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.528 Γ— 10⁹⁡(96-digit number)
25286017181978762814…49948111706714326399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.057 Γ— 10⁹⁡(96-digit number)
50572034363957525629…99896223413428652799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.011 Γ— 10⁹⁢(97-digit number)
10114406872791505125…99792446826857305599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.022 Γ— 10⁹⁢(97-digit number)
20228813745583010251…99584893653714611199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.045 Γ— 10⁹⁢(97-digit number)
40457627491166020503…99169787307429222399
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:57,969,274 XPMΒ·at block #6,840,616 Β· updates every 60s
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