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Block #1,866,186

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/26/2016, 12:23:57 AM Β· Difficulty 10.6930 Β· 4,965,854 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
895304e0a9242c7b55779cadbd6d37263eb5a89ae9c433b6c494f68e5beb8f10
View on Chainz β†—

Height

#1,866,186

Difficulty

10.692990

Transactions

1

Size

242 B

Version

2

Bits

0ab167c7

Nonce

44,772,524

Timestamp

11/26/2016, 12:23:57 AM

Confirmations

4,965,854

Mined by

⛏️ P2SHAMeY5ZrV7AqtjFwPLjnwr3BDd53veG96Ko

Merkle Root

edc40926fe8ef41b9ad36dd1de47621b5521e3a21ec4b84266cf8a8556e6fa36
Transactions (1)
Coinbaseedc40926fe8ef4…cf8a8556e6fa36
1 in β†’ 2 out8.7300 XPM152 B
AMeY5ZrV…3veG96KoALPu3s2c…EJXLjVFh
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.

1.926 Γ— 10⁹⁡(96-digit number)
19263043227501407646…16779514469342955989
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
1.926 Γ— 10⁹⁡(96-digit number)
19263043227501407646…16779514469342955989
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.852 Γ— 10⁹⁡(96-digit number)
38526086455002815293…33559028938685911979
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.705 Γ— 10⁹⁡(96-digit number)
77052172910005630586…67118057877371823959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.541 Γ— 10⁹⁢(97-digit number)
15410434582001126117…34236115754743647919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.082 Γ— 10⁹⁢(97-digit number)
30820869164002252234…68472231509487295839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.164 Γ— 10⁹⁢(97-digit number)
61641738328004504469…36944463018974591679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.232 Γ— 10⁹⁷(98-digit number)
12328347665600900893…73888926037949183359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.465 Γ— 10⁹⁷(98-digit number)
24656695331201801787…47777852075898366719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.931 Γ— 10⁹⁷(98-digit number)
49313390662403603575…95555704151796733439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.862 Γ— 10⁹⁷(98-digit number)
98626781324807207151…91111408303593466879
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:57,900,453 XPMΒ·at block #6,832,039 Β· updates every 60s
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