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Block #599,445

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/23/2014, 3:02:34 PM Β· Difficulty 10.9268 Β· 6,208,515 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
480b4aec208a01335a094b5dca49dac44beb9fdd27b3f4c5800ae2a0abe6f4fd
View on Chainz β†—

Height

#599,445

Difficulty

10.926783

Transactions

1

Size

208 B

Version

2

Bits

0aed41ad

Nonce

446,654,080

Timestamp

6/23/2014, 3:02:34 PM

Confirmations

6,208,515

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

477816d3099ae4babd9733ff2cf76441a13e7247badaec6ad5a8d1537283cae2
Transactions (1)
Coinbase477816d3099ae4…a8d1537283cae2
1 in β†’ 1 out8.3600 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.562 Γ— 10¹⁰⁰(101-digit number)
15622666480210291775…40546303605982699521
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
1.562 Γ— 10¹⁰⁰(101-digit number)
15622666480210291775…40546303605982699521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.124 Γ— 10¹⁰⁰(101-digit number)
31245332960420583551…81092607211965399041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.249 Γ— 10¹⁰⁰(101-digit number)
62490665920841167102…62185214423930798081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.249 Γ— 10¹⁰¹(102-digit number)
12498133184168233420…24370428847861596161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.499 Γ— 10¹⁰¹(102-digit number)
24996266368336466841…48740857695723192321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.999 Γ— 10¹⁰¹(102-digit number)
49992532736672933682…97481715391446384641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.998 Γ— 10¹⁰¹(102-digit number)
99985065473345867364…94963430782892769281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.999 Γ— 10¹⁰²(103-digit number)
19997013094669173472…89926861565785538561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.999 Γ— 10¹⁰²(103-digit number)
39994026189338346945…79853723131571077121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.998 Γ— 10¹⁰²(103-digit number)
79988052378676693891…59707446263142154241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.599 Γ— 10¹⁰³(104-digit number)
15997610475735338778…19414892526284308481
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:57,707,722 XPMΒ·at block #6,807,959 Β· updates every 60s
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