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Block #77,547

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/22/2013, 11:08:12 AM Β· Difficulty 9.1805 Β· 6,739,832 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
70daa651f2d211d298791ab7dc1b337fd162d6fa74ddb4b52118fb8b6a0cad34
View on Chainz β†—

Height

#77,547

Difficulty

9.180470

Transactions

1

Size

201 B

Version

2

Bits

092e334f

Nonce

84

Timestamp

7/22/2013, 11:08:12 AM

Confirmations

6,739,832

Mined by

⛏️ P2SHAcuRhoVunZmd7TM7Neh2VRFvWv6Pu86km9

Merkle Root

f481aa13ddb01748f42fe5a0ed589feae9305dc082b86bd025377018aff00a6d
Transactions (1)
Coinbasef481aa13ddb017…377018aff00a6d
1 in β†’ 1 out11.8500 XPM110 B
AcuRhoVu…6Pu86km9
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.

7.268 Γ— 10⁹⁷(98-digit number)
72680604768891367573…48234739789999523551
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
7.268 Γ— 10⁹⁷(98-digit number)
72680604768891367573…48234739789999523551
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.453 Γ— 10⁹⁸(99-digit number)
14536120953778273514…96469479579999047101
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.907 Γ— 10⁹⁸(99-digit number)
29072241907556547029…92938959159998094201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.814 Γ— 10⁹⁸(99-digit number)
58144483815113094058…85877918319996188401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.162 Γ— 10⁹⁹(100-digit number)
11628896763022618811…71755836639992376801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.325 Γ— 10⁹⁹(100-digit number)
23257793526045237623…43511673279984753601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.651 Γ— 10⁹⁹(100-digit number)
46515587052090475246…87023346559969507201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.303 Γ— 10⁹⁹(100-digit number)
93031174104180950493…74046693119939014401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.860 Γ— 10¹⁰⁰(101-digit number)
18606234820836190098…48093386239878028801
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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