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Block #131,753

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/24/2013, 12:06:59 PM Β· Difficulty 9.7857 Β· 6,684,967 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1a9a3069bb8bcd0192528fc584683511bef2a27cd9853538702f9f25b05648ca
View on Chainz β†—

Height

#131,753

Difficulty

9.785743

Transactions

2

Size

1.43 KB

Version

2

Bits

09c92676

Nonce

208,941

Timestamp

8/24/2013, 12:06:59 PM

Confirmations

6,684,967

Mined by

⛏️ P2SHAcWaRVY1RXusLDgjTYSowgNTeZ1NtxL61q

Merkle Root

58cb715313f91ff608ba41e7388b11a6406b7c44565edc008eb6842ffb194159
Transactions (2)
Coinbasef571174e6d8926…69f64054ebaa16
1 in β†’ 1 out10.4500 XPM109 B
AcWaRVY1…1NtxL61q
58cee8d1633741…55335d5646f12a
8 in β†’ 2 out1221.3946 XPM1.23 KB
Aa3rV16X…TVbcWbBdAMst5Voo…4yd9MjtL
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.

5.632 Γ— 10⁹⁷(98-digit number)
56327184357416643888…72094379812512140261
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
5.632 Γ— 10⁹⁷(98-digit number)
56327184357416643888…72094379812512140261
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.126 Γ— 10⁹⁸(99-digit number)
11265436871483328777…44188759625024280521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.253 Γ— 10⁹⁸(99-digit number)
22530873742966657555…88377519250048561041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.506 Γ— 10⁹⁸(99-digit number)
45061747485933315111…76755038500097122081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.012 Γ— 10⁹⁸(99-digit number)
90123494971866630222…53510077000194244161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.802 Γ— 10⁹⁹(100-digit number)
18024698994373326044…07020154000388488321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.604 Γ— 10⁹⁹(100-digit number)
36049397988746652088…14040308000776976641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.209 Γ— 10⁹⁹(100-digit number)
72098795977493304177…28080616001553953281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.441 Γ— 10¹⁰⁰(101-digit number)
14419759195498660835…56161232003107906561
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:57,777,884 XPMΒ·at block #6,816,719 Β· updates every 60s
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