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Block #3,506,345

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/9/2020, 6:18:38 AM Β· Difficulty 10.9305 Β· 3,336,808 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dafb2700f5e155d423e815db97ef465af9e444d9ca7105e794409c1c553f55e3
View on Chainz β†—

Height

#3,506,345

Difficulty

10.930509

Transactions

1

Size

201 B

Version

2

Bits

0aee35da

Nonce

29,585,429

Timestamp

1/9/2020, 6:18:38 AM

Confirmations

3,336,808

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

866100413bc23b293617586fa35c3f09bb1d71560d997b95214f6bae3ed0ca75
Transactions (1)
Coinbase866100413bc23b…4f6bae3ed0ca75
1 in β†’ 1 out8.3600 XPM110 B
ASiq2qtK…VMhmk7yL
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.

6.565 Γ— 10⁹⁢(97-digit number)
65655393183876419684…60382039712580437761
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
6.565 Γ— 10⁹⁢(97-digit number)
65655393183876419684…60382039712580437761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.313 Γ— 10⁹⁷(98-digit number)
13131078636775283936…20764079425160875521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.626 Γ— 10⁹⁷(98-digit number)
26262157273550567873…41528158850321751041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.252 Γ— 10⁹⁷(98-digit number)
52524314547101135747…83056317700643502081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.050 Γ— 10⁹⁸(99-digit number)
10504862909420227149…66112635401287004161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.100 Γ— 10⁹⁸(99-digit number)
21009725818840454299…32225270802574008321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.201 Γ— 10⁹⁸(99-digit number)
42019451637680908598…64450541605148016641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.403 Γ— 10⁹⁸(99-digit number)
84038903275361817196…28901083210296033281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.680 Γ— 10⁹⁹(100-digit number)
16807780655072363439…57802166420592066561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.361 Γ— 10⁹⁹(100-digit number)
33615561310144726878…15604332841184133121
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:57,989,590 XPMΒ·at block #6,843,152 Β· updates every 60s
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