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Block #148,481

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/3/2013, 6:47:33 PM Β· Difficulty 9.8544 Β· 6,658,661 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a48aedc7275f1c338416a62927f21ef156f957d2bfe7035fc1bf2bee36372d05
View on Chainz β†—

Height

#148,481

Difficulty

9.854394

Transactions

1

Size

198 B

Version

2

Bits

09dab98e

Nonce

66,707

Timestamp

9/3/2013, 6:47:33 PM

Confirmations

6,658,661

Mined by

⛏️ P2SHAM9R37qPciuhUNYvwcMUHTUsnwhm8dCX8m

Merkle Root

aadb2ac9cbe94c52a40abd95f7fb6d4797012e5a5dd7d50fdca16cfb5bad3ff5
Transactions (1)
Coinbaseaadb2ac9cbe94c…a16cfb5bad3ff5
1 in β†’ 1 out10.2800 XPM109 B
AM9R37qP…hm8dCX8m
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.

1.321 Γ— 10⁹³(94-digit number)
13217564551161520246…14400090199226473601
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
1.321 Γ— 10⁹³(94-digit number)
13217564551161520246…14400090199226473601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.643 Γ— 10⁹³(94-digit number)
26435129102323040492…28800180398452947201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.287 Γ— 10⁹³(94-digit number)
52870258204646080984…57600360796905894401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.057 Γ— 10⁹⁴(95-digit number)
10574051640929216196…15200721593811788801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.114 Γ— 10⁹⁴(95-digit number)
21148103281858432393…30401443187623577601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.229 Γ— 10⁹⁴(95-digit number)
42296206563716864787…60802886375247155201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.459 Γ— 10⁹⁴(95-digit number)
84592413127433729574…21605772750494310401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.691 Γ— 10⁹⁡(96-digit number)
16918482625486745914…43211545500988620801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.383 Γ— 10⁹⁡(96-digit number)
33836965250973491829…86423091001977241601
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:57,701,143 XPMΒ·at block #6,807,141 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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