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Block #2,856,822

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/27/2018, 7:11:08 AM Β· Difficulty 11.6903 Β· 3,979,577 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d1c164076df57dadb295d9c3da829307e3d44de065ebd44eea7c67b558ba1660
View on Chainz β†—

Height

#2,856,822

Difficulty

11.690318

Transactions

1

Size

200 B

Version

2

Bits

0bb0b8b6

Nonce

519,110,040

Timestamp

9/27/2018, 7:11:08 AM

Confirmations

3,979,577

Mined by

⛏️ P2SHAQYmGCSqes5T3wYCZG3PYZhvKMRJfngRCn

Merkle Root

28ecd76fabec15d74762a9e2957794a285bae89e9d54fc5254340d91ded6fb61
Transactions (1)
Coinbase28ecd76fabec15…340d91ded6fb61
1 in β†’ 1 out7.3000 XPM110 B
AQYmGCSq…RJfngRCn
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.

2.125 Γ— 10⁹⁴(95-digit number)
21254763496447680886…95385945279765583361
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
2.125 Γ— 10⁹⁴(95-digit number)
21254763496447680886…95385945279765583361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.250 Γ— 10⁹⁴(95-digit number)
42509526992895361772…90771890559531166721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.501 Γ— 10⁹⁴(95-digit number)
85019053985790723545…81543781119062333441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.700 Γ— 10⁹⁡(96-digit number)
17003810797158144709…63087562238124666881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.400 Γ— 10⁹⁡(96-digit number)
34007621594316289418…26175124476249333761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.801 Γ— 10⁹⁡(96-digit number)
68015243188632578836…52350248952498667521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.360 Γ— 10⁹⁢(97-digit number)
13603048637726515767…04700497904997335041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.720 Γ— 10⁹⁢(97-digit number)
27206097275453031534…09400995809994670081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.441 Γ— 10⁹⁢(97-digit number)
54412194550906063069…18801991619989340161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.088 Γ— 10⁹⁷(98-digit number)
10882438910181212613…37603983239978680321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.176 Γ— 10⁹⁷(98-digit number)
21764877820362425227…75207966479957360641
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:57,935,455 XPMΒ·at block #6,836,398 Β· updates every 60s
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