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Block #2,233,768

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/2/2017, 1:08:18 PM Β· Difficulty 10.9461 Β· 4,597,135 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6f62e34c2c57b60fb366b8165078a634c6798a9b5e4de927cb45940d9f5d75ee
View on Chainz β†—

Height

#2,233,768

Difficulty

10.946105

Transactions

1

Size

201 B

Version

2

Bits

0af233e9

Nonce

435,781,126

Timestamp

8/2/2017, 1:08:18 PM

Confirmations

4,597,135

Mined by

⛏️ P2SHAPCwu7ARQCLyVaepwuXZaPhJfxsfuZA3YV

Merkle Root

0be0d1fe1990a681132de22e01b4f1b9a7fe5be6474e98dc6c68171b94dfa446
Transactions (1)
Coinbase0be0d1fe1990a6…68171b94dfa446
1 in β†’ 1 out8.3300 XPM110 B
APCwu7AR…sfuZA3YV
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.

9.303 Γ— 10⁹⁢(97-digit number)
93036591761558619644…62764355834717921279
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
9.303 Γ— 10⁹⁢(97-digit number)
93036591761558619644…62764355834717921279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.860 Γ— 10⁹⁷(98-digit number)
18607318352311723928…25528711669435842559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.721 Γ— 10⁹⁷(98-digit number)
37214636704623447857…51057423338871685119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.442 Γ— 10⁹⁷(98-digit number)
74429273409246895715…02114846677743370239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.488 Γ— 10⁹⁸(99-digit number)
14885854681849379143…04229693355486740479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.977 Γ— 10⁹⁸(99-digit number)
29771709363698758286…08459386710973480959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.954 Γ— 10⁹⁸(99-digit number)
59543418727397516572…16918773421946961919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.190 Γ— 10⁹⁹(100-digit number)
11908683745479503314…33837546843893923839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.381 Γ— 10⁹⁹(100-digit number)
23817367490959006628…67675093687787847679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.763 Γ— 10⁹⁹(100-digit number)
47634734981918013257…35350187375575695359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.526 Γ— 10⁹⁹(100-digit number)
95269469963836026515…70700374751151390719
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:57,891,353 XPMΒ·at block #6,830,902 Β· updates every 60s
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