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Block #2,792,362

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/13/2018, 4:17:40 PM Β· Difficulty 11.6751 Β· 4,049,632 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8a8ce657fd3cd901c62e6963755da17d570ece3b91270acfa17ee660f95408eb
View on Chainz β†—

Height

#2,792,362

Difficulty

11.675093

Transactions

1

Size

201 B

Version

2

Bits

0bacd2ec

Nonce

743,942,589

Timestamp

8/13/2018, 4:17:40 PM

Confirmations

4,049,632

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

0075f3a313b6bd6ad15fa07124a5593811d582bde9688ab06a28024a97ddd9d6
Transactions (1)
Coinbase0075f3a313b6bd…28024a97ddd9d6
1 in β†’ 1 out7.3200 XPM110 B
AZtxQr2F…7grUWrUz
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.

8.234 Γ— 10⁹⁡(96-digit number)
82343875495918843139…39470717528855521281
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
8.234 Γ— 10⁹⁡(96-digit number)
82343875495918843139…39470717528855521281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.646 Γ— 10⁹⁢(97-digit number)
16468775099183768627…78941435057711042561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.293 Γ— 10⁹⁢(97-digit number)
32937550198367537255…57882870115422085121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.587 Γ— 10⁹⁢(97-digit number)
65875100396735074511…15765740230844170241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.317 Γ— 10⁹⁷(98-digit number)
13175020079347014902…31531480461688340481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.635 Γ— 10⁹⁷(98-digit number)
26350040158694029804…63062960923376680961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.270 Γ— 10⁹⁷(98-digit number)
52700080317388059609…26125921846753361921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.054 Γ— 10⁹⁸(99-digit number)
10540016063477611921…52251843693506723841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.108 Γ— 10⁹⁸(99-digit number)
21080032126955223843…04503687387013447681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.216 Γ— 10⁹⁸(99-digit number)
42160064253910447687…09007374774026895361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.432 Γ— 10⁹⁸(99-digit number)
84320128507820895374…18014749548053790721
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
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