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Block #161,443

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/12/2013, 4:18:47 PM Β· Difficulty 9.8593 Β· 6,646,819 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0dfd974438b42cfdc682be55f172b02d677e00569244ff2cfd5b91f376cedafc
View on Chainz β†—

Height

#161,443

Difficulty

9.859272

Transactions

1

Size

198 B

Version

2

Bits

09dbf93f

Nonce

231,443

Timestamp

9/12/2013, 4:18:47 PM

Confirmations

6,646,819

Mined by

⛏️ P2SHAM9R37qPciuhUNYvwcMUHTUsnwhm8dCX8m

Merkle Root

af2fb5e7ac4032cb1e230124e7373ea4dc8c25efdbb38735a0b8ee30e76d435c
Transactions (1)
Coinbaseaf2fb5e7ac4032…b8ee30e76d435c
1 in β†’ 1 out10.2700 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.

4.490 Γ— 10⁹²(93-digit number)
44906466665066313986…05395283394098865601
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
4.490 Γ— 10⁹²(93-digit number)
44906466665066313986…05395283394098865601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.981 Γ— 10⁹²(93-digit number)
89812933330132627972…10790566788197731201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.796 Γ— 10⁹³(94-digit number)
17962586666026525594…21581133576395462401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.592 Γ— 10⁹³(94-digit number)
35925173332053051189…43162267152790924801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.185 Γ— 10⁹³(94-digit number)
71850346664106102378…86324534305581849601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.437 Γ— 10⁹⁴(95-digit number)
14370069332821220475…72649068611163699201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.874 Γ— 10⁹⁴(95-digit number)
28740138665642440951…45298137222327398401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.748 Γ— 10⁹⁴(95-digit number)
57480277331284881902…90596274444654796801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.149 Γ— 10⁹⁡(96-digit number)
11496055466256976380…81192548889309593601
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:57,710,143 XPMΒ·at block #6,808,261 Β· updates every 60s
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