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Block #75,143

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/21/2013, 2:55:19 PM Β· Difficulty 8.9959 Β· 6,739,177 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e60f2ead1c7618fbb3820a85dbd10a420cbf99dfeddf38b3e649502fc4a2048e
View on Chainz β†—

Height

#75,143

Difficulty

8.995933

Transactions

1

Size

197 B

Version

2

Bits

08fef576

Nonce

351

Timestamp

7/21/2013, 2:55:19 PM

Confirmations

6,739,177

Mined by

⛏️ P2SHAPxUMipnp1rZxF8iz1xZQD73Wi2zpbPwcA

Merkle Root

f6c0ccc3588dff36f5a3aa559ccc65ebe294952864b1b220dd0808772919660a
Transactions (1)
Coinbasef6c0ccc3588dff…0808772919660a
1 in β†’ 1 out12.3400 XPM109 B
APxUMipn…2zpbPwcA
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.

6.146 Γ— 10⁸⁹(90-digit number)
61463033261895777143…28132664727459965599
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
6.146 Γ— 10⁸⁹(90-digit number)
61463033261895777143…28132664727459965599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.229 Γ— 10⁹⁰(91-digit number)
12292606652379155428…56265329454919931199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.458 Γ— 10⁹⁰(91-digit number)
24585213304758310857…12530658909839862399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.917 Γ— 10⁹⁰(91-digit number)
49170426609516621714…25061317819679724799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.834 Γ— 10⁹⁰(91-digit number)
98340853219033243429…50122635639359449599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.966 Γ— 10⁹¹(92-digit number)
19668170643806648685…00245271278718899199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.933 Γ— 10⁹¹(92-digit number)
39336341287613297371…00490542557437798399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.867 Γ— 10⁹¹(92-digit number)
78672682575226594743…00981085114875596799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.573 Γ— 10⁹²(93-digit number)
15734536515045318948…01962170229751193599
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,758,624 XPMΒ·at block #6,814,319 Β· updates every 60s
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