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Block #289,655

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/2/2013, 7:49:45 AM Β· Difficulty 9.9887 Β· 6,516,196 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
528b170aca9c2a68150a691ed91b742dc912ae106ca2fa84223dec8d373450f8
View on Chainz β†—

Height

#289,655

Difficulty

9.988658

Transactions

2

Size

869 B

Version

2

Bits

09fd18ae

Nonce

85,574

Timestamp

12/2/2013, 7:49:45 AM

Confirmations

6,516,196

Mined by

⛏️ P2SHAH1C2h2qNxFdJyfe1emFzheXx3qUwnVGoY

Merkle Root

71ce73284250ef6e6b7e7b8b1ed60148691b8ab0f72c2cad10f90228238229f7
Transactions (2)
Coinbase679a4045c4bae5…b41beb7f8ebed7
1 in β†’ 1 out10.0200 XPM109 B
AH1C2h2q…qUwnVGoY
c6578be7316090…db3ccb82273633
4 in β†’ 2 out4.8295 XPM669 B
AFxPxDn9…uFk2v6xgAJwbn52T…Mi9yBY4D
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.

1.995 Γ— 10⁹⁷(98-digit number)
19954567342571779268…13165620741780346881
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
1.995 Γ— 10⁹⁷(98-digit number)
19954567342571779268…13165620741780346881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.990 Γ— 10⁹⁷(98-digit number)
39909134685143558537…26331241483560693761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.981 Γ— 10⁹⁷(98-digit number)
79818269370287117075…52662482967121387521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.596 Γ— 10⁹⁸(99-digit number)
15963653874057423415…05324965934242775041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.192 Γ— 10⁹⁸(99-digit number)
31927307748114846830…10649931868485550081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.385 Γ— 10⁹⁸(99-digit number)
63854615496229693660…21299863736971100161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.277 Γ— 10⁹⁹(100-digit number)
12770923099245938732…42599727473942200321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.554 Γ— 10⁹⁹(100-digit number)
25541846198491877464…85199454947884400641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.108 Γ— 10⁹⁹(100-digit number)
51083692396983754928…70398909895768801281
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:57,690,888 XPMΒ·at block #6,805,850 Β· updates every 60s
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