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Block #152,383

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/6/2013, 7:19:08 AM Β· Difficulty 9.8622 Β· 6,642,954 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a4bbebbb52ebf658033fc056769db7a02759ec77a5de43105b3138d9220100aa
View on Chainz β†—

Height

#152,383

Difficulty

9.862167

Transactions

1

Size

200 B

Version

2

Bits

09dcb700

Nonce

36,856

Timestamp

9/6/2013, 7:19:08 AM

Confirmations

6,642,954

Mined by

⛏️ P2SHAKuN3h41uzqou2DMgdMaGXXiiCifcoaLP1

Merkle Root

50b6f0dce8980ed120ae363071dab3ddefeff274d7d5d099fb07aba7b7e0ccf9
Transactions (1)
Coinbase50b6f0dce8980e…07aba7b7e0ccf9
1 in β†’ 1 out10.2700 XPM109 B
AKuN3h41…ifcoaLP1
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.

3.355 Γ— 10⁹⁢(97-digit number)
33559395913789806545…84233487770173160959
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
3.355 Γ— 10⁹⁢(97-digit number)
33559395913789806545…84233487770173160959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.711 Γ— 10⁹⁢(97-digit number)
67118791827579613091…68466975540346321919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.342 Γ— 10⁹⁷(98-digit number)
13423758365515922618…36933951080692643839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.684 Γ— 10⁹⁷(98-digit number)
26847516731031845236…73867902161385287679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.369 Γ— 10⁹⁷(98-digit number)
53695033462063690473…47735804322770575359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.073 Γ— 10⁹⁸(99-digit number)
10739006692412738094…95471608645541150719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.147 Γ— 10⁹⁸(99-digit number)
21478013384825476189…90943217291082301439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.295 Γ— 10⁹⁸(99-digit number)
42956026769650952378…81886434582164602879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.591 Γ— 10⁹⁸(99-digit number)
85912053539301904757…63772869164329205759
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:57,606,755 XPMΒ·at block #6,795,336 Β· updates every 60s
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