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Block #156,388

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/8/2013, 10:21:53 PM Β· Difficulty 9.8683 Β· 6,657,624 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8a3c4a0d042c29bd6f9edf4a24a73eb00f1f5b461ba2d705b836b77d0837726d
View on Chainz β†—

Height

#156,388

Difficulty

9.868253

Transactions

1

Size

200 B

Version

2

Bits

09de45ce

Nonce

37,603

Timestamp

9/8/2013, 10:21:53 PM

Confirmations

6,657,624

Mined by

⛏️ P2SHARwEjnekTmEd4gDgSnACXGZ9UNXN12RHSr

Merkle Root

f03c8752f8bab71231e25faf797eb5181d0b2be9872314db90e59f0e1a9dd4e4
Transactions (1)
Coinbasef03c8752f8bab7…e59f0e1a9dd4e4
1 in β†’ 1 out10.2500 XPM109 B
ARwEjnek…XN12RHSr
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.

1.825 Γ— 10⁹⁢(97-digit number)
18252844285649674064…23529407621936587101
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
1.825 Γ— 10⁹⁢(97-digit number)
18252844285649674064…23529407621936587101
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.650 Γ— 10⁹⁢(97-digit number)
36505688571299348129…47058815243873174201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.301 Γ— 10⁹⁢(97-digit number)
73011377142598696258…94117630487746348401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.460 Γ— 10⁹⁷(98-digit number)
14602275428519739251…88235260975492696801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.920 Γ— 10⁹⁷(98-digit number)
29204550857039478503…76470521950985393601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.840 Γ— 10⁹⁷(98-digit number)
58409101714078957006…52941043901970787201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.168 Γ— 10⁹⁸(99-digit number)
11681820342815791401…05882087803941574401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.336 Γ— 10⁹⁸(99-digit number)
23363640685631582802…11764175607883148801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.672 Γ— 10⁹⁸(99-digit number)
46727281371263165605…23528351215766297601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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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