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Block #173,094

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/20/2013, 5:42:23 PM Β· Difficulty 9.8612 Β· 6,637,743 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f29fc6a307d63be75a5a42b74b919a9688241c7745fd64b363862666f1362ff1
View on Chainz β†—

Height

#173,094

Difficulty

9.861217

Transactions

1

Size

199 B

Version

2

Bits

09dc78b0

Nonce

1,077

Timestamp

9/20/2013, 5:42:23 PM

Confirmations

6,637,743

Mined by

⛏️ P2SHANHdEAYnG4HaHTdmo4u2875QdotWioiVGQ

Merkle Root

842ee3155df57cbb3c4c361a6de1a0d63392e1d2e17b911161b7b909926ce1b6
Transactions (1)
Coinbase842ee3155df57c…b7b909926ce1b6
1 in β†’ 1 out10.2700 XPM109 B
ANHdEAYn…tWioiVGQ
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.

2.768 Γ— 10⁹⁴(95-digit number)
27681301441838799396…48007638261945048321
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
2.768 Γ— 10⁹⁴(95-digit number)
27681301441838799396…48007638261945048321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.536 Γ— 10⁹⁴(95-digit number)
55362602883677598793…96015276523890096641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.107 Γ— 10⁹⁡(96-digit number)
11072520576735519758…92030553047780193281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.214 Γ— 10⁹⁡(96-digit number)
22145041153471039517…84061106095560386561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.429 Γ— 10⁹⁡(96-digit number)
44290082306942079035…68122212191120773121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.858 Γ— 10⁹⁡(96-digit number)
88580164613884158070…36244424382241546241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.771 Γ— 10⁹⁢(97-digit number)
17716032922776831614…72488848764483092481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.543 Γ— 10⁹⁢(97-digit number)
35432065845553663228…44977697528966184961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.086 Γ— 10⁹⁢(97-digit number)
70864131691107326456…89955395057932369921
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
Circulating Supply:57,730,792 XPMΒ·at block #6,810,836 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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