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Block #2,635,361

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/29/2018, 5:35:34 AM Β· Difficulty 11.3095 Β· 4,207,428 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2f6da898efdc9125c3f23b8a1215bcb0b5ffb13cb6d767f5216081f54a16a7d4
View on Chainz β†—

Height

#2,635,361

Difficulty

11.309474

Transactions

2

Size

427 B

Version

2

Bits

0b4f39a9

Nonce

179,921,202

Timestamp

4/29/2018, 5:35:34 AM

Confirmations

4,207,428

Mined by

⛏️ P2SHALLjQki5ACyjThjaKbLmfSNbDtdMpjcPQo

Merkle Root

23ca5a815720bb758d5c4a8e19fcb18a691f108b67af4175e70df14588843339
Transactions (2)
Coinbase3e17ea7e573033…04ff9362f7cdee
1 in β†’ 1 out7.8200 XPM110 B
ALLjQki5…dMpjcPQo
c4af060c5b166d…9dfa5b1b1b2583
1 in β†’ 2 out28460.5005 XPM227 B
AQ23ba76…ApJuowg9AU7xkW52…RMPvkSaU
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.

1.006 Γ— 10⁹⁴(95-digit number)
10065288182241270428…30652102508194691851
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
1.006 Γ— 10⁹⁴(95-digit number)
10065288182241270428…30652102508194691851
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.013 Γ— 10⁹⁴(95-digit number)
20130576364482540857…61304205016389383701
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.026 Γ— 10⁹⁴(95-digit number)
40261152728965081715…22608410032778767401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.052 Γ— 10⁹⁴(95-digit number)
80522305457930163431…45216820065557534801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.610 Γ— 10⁹⁡(96-digit number)
16104461091586032686…90433640131115069601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.220 Γ— 10⁹⁡(96-digit number)
32208922183172065372…80867280262230139201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.441 Γ— 10⁹⁡(96-digit number)
64417844366344130744…61734560524460278401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.288 Γ— 10⁹⁢(97-digit number)
12883568873268826148…23469121048920556801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.576 Γ— 10⁹⁢(97-digit number)
25767137746537652297…46938242097841113601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.153 Γ— 10⁹⁢(97-digit number)
51534275493075304595…93876484195682227201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.030 Γ— 10⁹⁷(98-digit number)
10306855098615060919…87752968391364454401
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:57,986,650 XPMΒ·at block #6,842,788 Β· updates every 60s
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