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Block #253,711

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/10/2013, 7:36:37 AM Β· Difficulty 9.9724 Β· 6,556,055 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
aa99411db698db378719a79498f015eb1a7f80841b48d737c7c4fbbb1b0d4beb
View on Chainz β†—

Height

#253,711

Difficulty

9.972383

Transactions

1

Size

201 B

Version

2

Bits

09f8ee1a

Nonce

4,587

Timestamp

11/10/2013, 7:36:37 AM

Confirmations

6,556,055

Mined by

⛏️ P2SHATS8xg29vBkCkcqpeLDxUSUf8b9XrErcvd

Merkle Root

c7f575ac5796c2ca87a5e9fe28a96ea8dc54835c97f91b3ee819b886f916a84c
Transactions (1)
Coinbasec7f575ac5796c2…19b886f916a84c
1 in β†’ 1 out10.0400 XPM109 B
ATS8xg29…9XrErcvd
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.

1.402 Γ— 10⁹⁹(100-digit number)
14029766214308058570…97815351164926771201
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
1.402 Γ— 10⁹⁹(100-digit number)
14029766214308058570…97815351164926771201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.805 Γ— 10⁹⁹(100-digit number)
28059532428616117140…95630702329853542401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.611 Γ— 10⁹⁹(100-digit number)
56119064857232234281…91261404659707084801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.122 Γ— 10¹⁰⁰(101-digit number)
11223812971446446856…82522809319414169601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.244 Γ— 10¹⁰⁰(101-digit number)
22447625942892893712…65045618638828339201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.489 Γ— 10¹⁰⁰(101-digit number)
44895251885785787425…30091237277656678401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.979 Γ— 10¹⁰⁰(101-digit number)
89790503771571574850…60182474555313356801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.795 Γ— 10¹⁰¹(102-digit number)
17958100754314314970…20364949110626713601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.591 Γ— 10¹⁰¹(102-digit number)
35916201508628629940…40729898221253427201
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:57,722,214 XPMΒ·at block #6,809,765 Β· updates every 60s
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