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Block #154,562

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/7/2013, 6:11:46 PM Β· Difficulty 9.8646 Β· 6,650,332 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
59d9e5ec718c6f9ba691a00bfad5fe4303633de06099d2de7da8047f0f1697e6
View on Chainz β†—

Height

#154,562

Difficulty

9.864603

Transactions

1

Size

197 B

Version

2

Bits

09dd56a4

Nonce

111,273

Timestamp

9/7/2013, 6:11:46 PM

Confirmations

6,650,332

Mined by

⛏️ P2SHATr36r6GPrDWuY8aErt6RmRFsBKgmGvw5f

Merkle Root

e14105f6cea95eb55f74280d447ba5074721c732d0f03335ea8f935b868a5473
Transactions (1)
Coinbasee14105f6cea95e…8f935b868a5473
1 in β†’ 1 out10.2600 XPM109 B
ATr36r6G…KgmGvw5f
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.

9.232 Γ— 10⁸⁹(90-digit number)
92324110904297683186…22498192503199740879
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
9.232 Γ— 10⁸⁹(90-digit number)
92324110904297683186…22498192503199740879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.846 Γ— 10⁹⁰(91-digit number)
18464822180859536637…44996385006399481759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.692 Γ— 10⁹⁰(91-digit number)
36929644361719073274…89992770012798963519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.385 Γ— 10⁹⁰(91-digit number)
73859288723438146549…79985540025597927039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.477 Γ— 10⁹¹(92-digit number)
14771857744687629309…59971080051195854079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.954 Γ— 10⁹¹(92-digit number)
29543715489375258619…19942160102391708159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.908 Γ— 10⁹¹(92-digit number)
59087430978750517239…39884320204783416319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.181 Γ— 10⁹²(93-digit number)
11817486195750103447…79768640409566832639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.363 Γ— 10⁹²(93-digit number)
23634972391500206895…59537280819133665279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.726 Γ— 10⁹²(93-digit number)
47269944783000413791…19074561638267330559
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,683,230 XPMΒ·at block #6,804,893 Β· updates every 60s
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