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Block #163,145

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/13/2013, 7:30:35 PM Β· Difficulty 9.8612 Β· 6,631,729 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6235658bb3267d89b83fb88b0d86c8aaa1e76ef41d908d675725dbab270f656a
View on Chainz β†—

Height

#163,145

Difficulty

9.861250

Transactions

1

Size

198 B

Version

2

Bits

09dc7ade

Nonce

63,410

Timestamp

9/13/2013, 7:30:35 PM

Confirmations

6,631,729

Mined by

⛏️ P2SHAdDUNTYmz3S4v6JdhjgL2fyWhUv4Zjqa77

Merkle Root

15920064751eb34752cded9e87a436bd50f478bd229296dc4b2c06e3920c98b3
Transactions (1)
Coinbase15920064751eb3…2c06e3920c98b3
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.

1.662 Γ— 10⁹²(93-digit number)
16624782514648235068…82729020904032518401
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
1.662 Γ— 10⁹²(93-digit number)
16624782514648235068…82729020904032518401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.324 Γ— 10⁹²(93-digit number)
33249565029296470137…65458041808065036801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.649 Γ— 10⁹²(93-digit number)
66499130058592940275…30916083616130073601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.329 Γ— 10⁹³(94-digit number)
13299826011718588055…61832167232260147201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.659 Γ— 10⁹³(94-digit number)
26599652023437176110…23664334464520294401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.319 Γ— 10⁹³(94-digit number)
53199304046874352220…47328668929040588801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.063 Γ— 10⁹⁴(95-digit number)
10639860809374870444…94657337858081177601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.127 Γ— 10⁹⁴(95-digit number)
21279721618749740888…89314675716162355201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.255 Γ— 10⁹⁴(95-digit number)
42559443237499481776…78629351432324710401
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:57,603,025 XPMΒ·at block #6,794,873 Β· updates every 60s
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