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Block #3,503,462

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/7/2020, 5:53:47 AM Β· Difficulty 10.9307 Β· 3,334,376 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
82ee914349f7a0773d73d09694f3fe4af31f192a00d22cffa9a11a6e7a2b5be6
View on Chainz β†—

Height

#3,503,462

Difficulty

10.930724

Transactions

2

Size

7.47 KB

Version

2

Bits

0aee43f1

Nonce

310,518,629

Timestamp

1/7/2020, 5:53:47 AM

Confirmations

3,334,376

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

9b628f08a8b9ad98fac0607b7bc621059e80b689d0389ee8ae264eb2aeefad4b
Transactions (2)
Coinbase4810d49ceb1980…41679d615b743f
1 in β†’ 1 out8.4400 XPM110 B
ASiq2qtK…VMhmk7yL
393adfa8671a0b…fc0d4c3ac1f289
50 in β†’ 1 out499.9200 XPM7.28 KB
ALcTQaSP…1C5Yf2Zi
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.

5.759 Γ— 10⁹³(94-digit number)
57599355520741861254…27848783465102370841
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
5.759 Γ— 10⁹³(94-digit number)
57599355520741861254…27848783465102370841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.151 Γ— 10⁹⁴(95-digit number)
11519871104148372250…55697566930204741681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.303 Γ— 10⁹⁴(95-digit number)
23039742208296744501…11395133860409483361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.607 Γ— 10⁹⁴(95-digit number)
46079484416593489003…22790267720818966721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.215 Γ— 10⁹⁴(95-digit number)
92158968833186978007…45580535441637933441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.843 Γ— 10⁹⁡(96-digit number)
18431793766637395601…91161070883275866881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.686 Γ— 10⁹⁡(96-digit number)
36863587533274791202…82322141766551733761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.372 Γ— 10⁹⁡(96-digit number)
73727175066549582405…64644283533103467521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.474 Γ— 10⁹⁢(97-digit number)
14745435013309916481…29288567066206935041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.949 Γ— 10⁹⁢(97-digit number)
29490870026619832962…58577134132413870081
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,947,047 XPMΒ·at block #6,837,837 Β· updates every 60s
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