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Block #157,095

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/9/2013, 9:52:46 AM Β· Difficulty 9.8688 Β· 6,649,791 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
88346ddc41ef6aa70e712a722a66dca18dda7bd53d16e1984687a858d8ea1af5
View on Chainz β†—

Height

#157,095

Difficulty

9.868764

Transactions

1

Size

197 B

Version

2

Bits

09de6758

Nonce

883,377

Timestamp

9/9/2013, 9:52:46 AM

Confirmations

6,649,791

Mined by

⛏️ P2SHAHiscA3WFz9dnGf3xRFCFqJkKatvPD5RmV

Merkle Root

9d44448ef4fcff90dbacb4fe49f4ec4135b09f0e1a9a1572f8c8178f18ba6171
Transactions (1)
Coinbase9d44448ef4fcff…c8178f18ba6171
1 in β†’ 1 out10.2500 XPM109 B
AHiscA3W…tvPD5RmV
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.

2.703 Γ— 10⁹⁰(91-digit number)
27035578898925284205…82137655962947687801
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
2.703 Γ— 10⁹⁰(91-digit number)
27035578898925284205…82137655962947687801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.407 Γ— 10⁹⁰(91-digit number)
54071157797850568411…64275311925895375601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.081 Γ— 10⁹¹(92-digit number)
10814231559570113682…28550623851790751201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.162 Γ— 10⁹¹(92-digit number)
21628463119140227364…57101247703581502401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.325 Γ— 10⁹¹(92-digit number)
43256926238280454728…14202495407163004801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.651 Γ— 10⁹¹(92-digit number)
86513852476560909457…28404990814326009601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.730 Γ— 10⁹²(93-digit number)
17302770495312181891…56809981628652019201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.460 Γ— 10⁹²(93-digit number)
34605540990624363783…13619963257304038401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.921 Γ— 10⁹²(93-digit number)
69211081981248727566…27239926514608076801
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:57,699,195 XPMΒ·at block #6,806,885 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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