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Block #209,051

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/14/2013, 8:58:32 AM Β· Difficulty 9.9082 Β· 6,594,510 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dc9564a053d0d6d18479cca970161cc1f7b11ce6ab0ee929424f94820c255421
View on Chainz β†—

Height

#209,051

Difficulty

9.908153

Transactions

1

Size

200 B

Version

2

Bits

09e87cbd

Nonce

18,327

Timestamp

10/14/2013, 8:58:32 AM

Confirmations

6,594,510

Mined by

⛏️ P2SHARBRYiL8QjnU5zrwTmS3JgwVXJoj38gY3N

Merkle Root

80f45a28e1123f67a7206e9ddfb93ea0006b61b0a86c4a63faa5c8c33cdc035f
Transactions (1)
Coinbase80f45a28e1123f…a5c8c33cdc035f
1 in β†’ 1 out10.1700 XPM109 B
ARBRYiL8…oj38gY3N
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.

1.471 Γ— 10⁹⁷(98-digit number)
14716816199202856245…59428480559381565439
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
1.471 Γ— 10⁹⁷(98-digit number)
14716816199202856245…59428480559381565439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.943 Γ— 10⁹⁷(98-digit number)
29433632398405712490…18856961118763130879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.886 Γ— 10⁹⁷(98-digit number)
58867264796811424981…37713922237526261759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.177 Γ— 10⁹⁸(99-digit number)
11773452959362284996…75427844475052523519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.354 Γ— 10⁹⁸(99-digit number)
23546905918724569992…50855688950105047039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.709 Γ— 10⁹⁸(99-digit number)
47093811837449139985…01711377900210094079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.418 Γ— 10⁹⁸(99-digit number)
94187623674898279970…03422755800420188159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.883 Γ— 10⁹⁹(100-digit number)
18837524734979655994…06845511600840376319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.767 Γ— 10⁹⁹(100-digit number)
37675049469959311988…13691023201680752639
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:57,672,520 XPMΒ·at block #6,803,560 Β· updates every 60s
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