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Block #149,943

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/4/2013, 5:05:18 PM Β· Difficulty 9.8581 Β· 6,656,031 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3278f9312bae5fe7d60185c5e1f846ac45bd8ae14f79fabb7645687c25c4ce72
View on Chainz β†—

Height

#149,943

Difficulty

9.858061

Transactions

1

Size

197 B

Version

2

Bits

09dba9dd

Nonce

433,010

Timestamp

9/4/2013, 5:05:18 PM

Confirmations

6,656,031

Mined by

⛏️ P2SHAbJsT1MFiTkk7HZiVSZy3MgHLJpF3oUXHW

Merkle Root

94daf1494b33be44c4096e15621f2c6368477f71024fb661cab03184b9dedb59
Transactions (1)
Coinbase94daf1494b33be…b03184b9dedb59
1 in β†’ 1 out10.2700 XPM109 B
AbJsT1MF…pF3oUXHW
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.

7.940 Γ— 10⁹⁰(91-digit number)
79406994758708105248…27887831737042016601
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
7.940 Γ— 10⁹⁰(91-digit number)
79406994758708105248…27887831737042016601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.588 Γ— 10⁹¹(92-digit number)
15881398951741621049…55775663474084033201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.176 Γ— 10⁹¹(92-digit number)
31762797903483242099…11551326948168066401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.352 Γ— 10⁹¹(92-digit number)
63525595806966484198…23102653896336132801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.270 Γ— 10⁹²(93-digit number)
12705119161393296839…46205307792672265601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.541 Γ— 10⁹²(93-digit number)
25410238322786593679…92410615585344531201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.082 Γ— 10⁹²(93-digit number)
50820476645573187358…84821231170689062401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.016 Γ— 10⁹³(94-digit number)
10164095329114637471…69642462341378124801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.032 Γ— 10⁹³(94-digit number)
20328190658229274943…39284924682756249601
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:57,691,867 XPMΒ·at block #6,805,973 Β· updates every 60s
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