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Block #1,612,571

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/3/2016, 4:26:47 PM Β· Difficulty 10.6010 Β· 5,230,380 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0b84a760aa51b6eac6c4170b5a192228015894dcfbfb3cf3026443901a177f2e
View on Chainz β†—

Height

#1,612,571

Difficulty

10.600967

Transactions

1

Size

200 B

Version

2

Bits

0a99d8f2

Nonce

1,273,917,396

Timestamp

6/3/2016, 4:26:47 PM

Confirmations

5,230,380

Mined by

⛏️ P2SHAcJCFN7fjf1XEUiVZPCwCKtxsoD6C1DRLd

Merkle Root

102269efc57c55465cdea18cdff243426d6cb798ad818c22a04f665361eba0ea
Transactions (1)
Coinbase102269efc57c55…4f665361eba0ea
1 in β†’ 1 out8.8800 XPM109 B
AcJCFN7f…D6C1DRLd
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.

9.777 Γ— 10⁹⁡(96-digit number)
97779164197479017793…00610353091497756161
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
9.777 Γ— 10⁹⁡(96-digit number)
97779164197479017793…00610353091497756161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.955 Γ— 10⁹⁢(97-digit number)
19555832839495803558…01220706182995512321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.911 Γ— 10⁹⁢(97-digit number)
39111665678991607117…02441412365991024641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.822 Γ— 10⁹⁢(97-digit number)
78223331357983214234…04882824731982049281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.564 Γ— 10⁹⁷(98-digit number)
15644666271596642846…09765649463964098561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.128 Γ— 10⁹⁷(98-digit number)
31289332543193285693…19531298927928197121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.257 Γ— 10⁹⁷(98-digit number)
62578665086386571387…39062597855856394241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.251 Γ— 10⁹⁸(99-digit number)
12515733017277314277…78125195711712788481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.503 Γ— 10⁹⁸(99-digit number)
25031466034554628555…56250391423425576961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.006 Γ— 10⁹⁸(99-digit number)
50062932069109257110…12500782846851153921
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
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