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Block #2,635,324

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/29/2018, 5:16:23 AM Β· Difficulty 11.3068 Β· 4,198,473 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
966130cb5f55c90ce284cd4ce90ee6a703247462ffc78245c4cbd52115517cc7
View on Chainz β†—

Height

#2,635,324

Difficulty

11.306800

Transactions

1

Size

200 B

Version

2

Bits

0b4e8a76

Nonce

721,901,763

Timestamp

4/29/2018, 5:16:23 AM

Confirmations

4,198,473

Mined by

⛏️ P2SHAZsS6yvbnaowQNAB8CnSn7jXLCnbsfpfsE

Merkle Root

bf3a3ab32466028fe0d4f571f6f2f53bf79257a36a81069f971ddbd6a20a15fb
Transactions (1)
Coinbasebf3a3ab3246602…1ddbd6a20a15fb
1 in β†’ 1 out7.8100 XPM110 B
AZsS6yvb…nbsfpfsE
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.

6.250 Γ— 10⁹³(94-digit number)
62505137673453518571…94653845016381586519
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
6.250 Γ— 10⁹³(94-digit number)
62505137673453518571…94653845016381586519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.250 Γ— 10⁹⁴(95-digit number)
12501027534690703714…89307690032763173039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.500 Γ— 10⁹⁴(95-digit number)
25002055069381407428…78615380065526346079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.000 Γ— 10⁹⁴(95-digit number)
50004110138762814857…57230760131052692159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.000 Γ— 10⁹⁡(96-digit number)
10000822027752562971…14461520262105384319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.000 Γ— 10⁹⁡(96-digit number)
20001644055505125942…28923040524210768639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.000 Γ— 10⁹⁡(96-digit number)
40003288111010251885…57846081048421537279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.000 Γ— 10⁹⁡(96-digit number)
80006576222020503771…15692162096843074559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.600 Γ— 10⁹⁢(97-digit number)
16001315244404100754…31384324193686149119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.200 Γ— 10⁹⁢(97-digit number)
32002630488808201508…62768648387372298239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.400 Γ— 10⁹⁢(97-digit number)
64005260977616403017…25537296774744596479
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:57,914,598 XPMΒ·at block #6,833,796 Β· updates every 60s
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