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Block #166,184

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/15/2013, 6:34:01 PM Β· Difficulty 9.8672 Β· 6,650,511 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bb2ab68a22452262f00af22c5612c04b6bfa84ae146bc91d6ad8e1903ed33792
View on Chainz β†—

Height

#166,184

Difficulty

9.867152

Transactions

1

Size

199 B

Version

2

Bits

09ddfda9

Nonce

78,406

Timestamp

9/15/2013, 6:34:01 PM

Confirmations

6,650,511

Mined by

⛏️ P2SHAK1PxfmQML85qBomVuaSRengfuqpq8MjPH

Merkle Root

bd956cd405a30deb5b98e0e67ce6d4964156c862a5a879edcb6d0fb571c63f84
Transactions (1)
Coinbasebd956cd405a30d…6d0fb571c63f84
1 in β†’ 1 out10.2600 XPM109 B
AK1PxfmQ…qpq8MjPH
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.

1.249 Γ— 10⁹⁴(95-digit number)
12494719179659695975…27598160434260260521
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
1.249 Γ— 10⁹⁴(95-digit number)
12494719179659695975…27598160434260260521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.498 Γ— 10⁹⁴(95-digit number)
24989438359319391950…55196320868520521041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.997 Γ— 10⁹⁴(95-digit number)
49978876718638783901…10392641737041042081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.995 Γ— 10⁹⁴(95-digit number)
99957753437277567802…20785283474082084161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.999 Γ— 10⁹⁡(96-digit number)
19991550687455513560…41570566948164168321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.998 Γ— 10⁹⁡(96-digit number)
39983101374911027121…83141133896328336641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.996 Γ— 10⁹⁡(96-digit number)
79966202749822054242…66282267792656673281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.599 Γ— 10⁹⁢(97-digit number)
15993240549964410848…32564535585313346561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.198 Γ— 10⁹⁢(97-digit number)
31986481099928821696…65129071170626693121
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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