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Block #161,250

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/12/2013, 1:12:48 PM Β· Difficulty 9.8590 Β· 6,642,107 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
610074adc7a2960438086404973453369a84c2b7049d917d37e318c40a466d15
View on Chainz β†—

Height

#161,250

Difficulty

9.859035

Transactions

1

Size

200 B

Version

2

Bits

09dbe9b9

Nonce

23,292

Timestamp

9/12/2013, 1:12:48 PM

Confirmations

6,642,107

Mined by

⛏️ P2SHAdDUNTYmz3S4v6JdhjgL2fyWhUv4Zjqa77

Merkle Root

ab4233f5aa6f37efd8eae9695e9999fa4b208146d5fe7f93c378488b0df78f36
Transactions (1)
Coinbaseab4233f5aa6f37…78488b0df78f36
1 in β†’ 1 out10.2700 XPM109 B
AdDUNTYm…v4Zjqa77
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.

1.076 Γ— 10⁹⁸(99-digit number)
10763041219807243658…94307716829127408641
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
1.076 Γ— 10⁹⁸(99-digit number)
10763041219807243658…94307716829127408641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.152 Γ— 10⁹⁸(99-digit number)
21526082439614487317…88615433658254817281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.305 Γ— 10⁹⁸(99-digit number)
43052164879228974634…77230867316509634561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.610 Γ— 10⁹⁸(99-digit number)
86104329758457949268…54461734633019269121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.722 Γ— 10⁹⁹(100-digit number)
17220865951691589853…08923469266038538241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.444 Γ— 10⁹⁹(100-digit number)
34441731903383179707…17846938532077076481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.888 Γ— 10⁹⁹(100-digit number)
68883463806766359414…35693877064154152961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.377 Γ— 10¹⁰⁰(101-digit number)
13776692761353271882…71387754128308305921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.755 Γ— 10¹⁰⁰(101-digit number)
27553385522706543765…42775508256616611841
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:57,670,891 XPMΒ·at block #6,803,356 Β· updates every 60s
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