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Block #2,190,822

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/3/2017, 9:03:53 AM Β· Difficulty 10.9499 Β· 4,636,155 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
de7515c82bd99b60d0ad2e0f8281b7d93d5d45b5d5563a0b42d2ded76fac8b6f
View on Chainz β†—

Height

#2,190,822

Difficulty

10.949937

Transactions

2

Size

869 B

Version

2

Bits

0af32f12

Nonce

20,012,263

Timestamp

7/3/2017, 9:03:53 AM

Confirmations

4,636,155

Mined by

⛏️ P2SHAeP7NEf9Lc3WkaQSrxbqgbMUNxemRF7Dfk

Merkle Root

1a2af9f7aba361d866d1dada2aec255bfc9017805d9022c45ac9950d0b5d58b4
Transactions (2)
Coinbase5f8e1c8f620e27…1ab97b68bd8423
1 in β†’ 1 out8.3400 XPM110 B
AeP7NEf9…emRF7Dfk
069b450098e931…ad6829bf9c82fb
4 in β†’ 2 out648.8027 XPM669 B
AdLv38Pf…k1z3e6DcAL4gLYnP…gDaxRWMQ
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.

1.483 Γ— 10⁹⁡(96-digit number)
14835048539532549071…03126075144683951999
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
1.483 Γ— 10⁹⁡(96-digit number)
14835048539532549071…03126075144683951999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.967 Γ— 10⁹⁡(96-digit number)
29670097079065098143…06252150289367903999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.934 Γ— 10⁹⁡(96-digit number)
59340194158130196286…12504300578735807999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.186 Γ— 10⁹⁢(97-digit number)
11868038831626039257…25008601157471615999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.373 Γ— 10⁹⁢(97-digit number)
23736077663252078514…50017202314943231999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.747 Γ— 10⁹⁢(97-digit number)
47472155326504157029…00034404629886463999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.494 Γ— 10⁹⁢(97-digit number)
94944310653008314058…00068809259772927999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.898 Γ— 10⁹⁷(98-digit number)
18988862130601662811…00137618519545855999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.797 Γ— 10⁹⁷(98-digit number)
37977724261203325623…00275237039091711999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.595 Γ— 10⁹⁷(98-digit number)
75955448522406651246…00550474078183423999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.519 Γ— 10⁹⁸(99-digit number)
15191089704481330249…01100948156366847999
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:57,859,991 XPMΒ·at block #6,826,976 Β· updates every 60s
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