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Block #154,125

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/7/2013, 11:20:30 AM Β· Difficulty 9.8639 Β· 6,660,063 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
85fea253bbdb71f15fb4cf9aa66e5b4f2fb491e62a621dec6a4266512ebe741a
View on Chainz β†—

Height

#154,125

Difficulty

9.863924

Transactions

2

Size

925 B

Version

2

Bits

09dd2a20

Nonce

100,763

Timestamp

9/7/2013, 11:20:30 AM

Confirmations

6,660,063

Mined by

⛏️ P2SHAQGz9h1x7euuJVUVqRVhcyEPS83RpsqhCW

Merkle Root

493e193321a94e0da3044bfa0cc681cc88f75d7343b3f63d04160b1767eb189b
Transactions (2)
Coinbase8cc28aedcd497c…abf9b299e0e372
1 in β†’ 1 out10.2700 XPM109 B
AQGz9h1x…3RpsqhCW
0408cfb5986256…4a8e0bee485436
6 in β†’ 1 out62.0100 XPM727 B
ASbV3iJo…cNNrV3WP
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.

2.102 Γ— 10⁹³(94-digit number)
21029198181752274712…07644122363014516801
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
2.102 Γ— 10⁹³(94-digit number)
21029198181752274712…07644122363014516801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.205 Γ— 10⁹³(94-digit number)
42058396363504549425…15288244726029033601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.411 Γ— 10⁹³(94-digit number)
84116792727009098850…30576489452058067201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.682 Γ— 10⁹⁴(95-digit number)
16823358545401819770…61152978904116134401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.364 Γ— 10⁹⁴(95-digit number)
33646717090803639540…22305957808232268801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.729 Γ— 10⁹⁴(95-digit number)
67293434181607279080…44611915616464537601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.345 Γ— 10⁹⁡(96-digit number)
13458686836321455816…89223831232929075201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.691 Γ— 10⁹⁡(96-digit number)
26917373672642911632…78447662465858150401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.383 Γ— 10⁹⁡(96-digit number)
53834747345285823264…56895324931716300801
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:57,757,577 XPMΒ·at block #6,814,187 Β· updates every 60s
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