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Block #2,077,869

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/19/2017, 2:53:42 PM Β· Difficulty 10.8513 Β· 4,758,943 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
79b4db329fd2807e21cd01270c56dd1471fc802e02deb2b9ec1fb5973f606062
View on Chainz β†—

Height

#2,077,869

Difficulty

10.851277

Transactions

1

Size

208 B

Version

2

Bits

0ad9ed45

Nonce

296,824,677

Timestamp

4/19/2017, 2:53:42 PM

Confirmations

4,758,943

Mined by

⛏️ P2SHAM6GYpjwZFjhLNzHZAfmRp8jwiaw86QDtR

Merkle Root

8f98c09e82cdfa852ebbad51f3e4ec34f501a2591cf5c590d0bc4d24648e3f07
Transactions (1)
Coinbase8f98c09e82cdfa…bc4d24648e3f07
1 in β†’ 1 out8.4800 XPM118 B
AM6GYpjw…aw86QDtR
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.

4.215 Γ— 10⁹⁴(95-digit number)
42158340639903283502…30318090491647279401
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
4.215 Γ— 10⁹⁴(95-digit number)
42158340639903283502…30318090491647279401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.431 Γ— 10⁹⁴(95-digit number)
84316681279806567004…60636180983294558801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.686 Γ— 10⁹⁡(96-digit number)
16863336255961313400…21272361966589117601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.372 Γ— 10⁹⁡(96-digit number)
33726672511922626801…42544723933178235201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.745 Γ— 10⁹⁡(96-digit number)
67453345023845253603…85089447866356470401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.349 Γ— 10⁹⁢(97-digit number)
13490669004769050720…70178895732712940801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.698 Γ— 10⁹⁢(97-digit number)
26981338009538101441…40357791465425881601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.396 Γ— 10⁹⁢(97-digit number)
53962676019076202882…80715582930851763201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.079 Γ— 10⁹⁷(98-digit number)
10792535203815240576…61431165861703526401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.158 Γ— 10⁹⁷(98-digit number)
21585070407630481153…22862331723407052801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.317 Γ— 10⁹⁷(98-digit number)
43170140815260962306…45724663446814105601
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
Circulating Supply:57,938,780 XPMΒ·at block #6,836,811 Β· updates every 60s
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