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Block #212,283

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/16/2013, 4:52:43 AM Β· Difficulty 9.9186 Β· 6,605,346 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ed93aebdb242566b020ecd17d5158ba53d02816e570440c37ad3446d35805324
View on Chainz β†—

Height

#212,283

Difficulty

9.918606

Transactions

1

Size

200 B

Version

2

Bits

09eb29c0

Nonce

119,453

Timestamp

10/16/2013, 4:52:43 AM

Confirmations

6,605,346

Mined by

⛏️ P2SHAdaUfNWzq3psoSPVfa6fSAEcYr3GgD9yxT

Merkle Root

21798d9e740a69f10b95172ce1923931b697c035ab009a3a3fe6537a6e41070b
Transactions (1)
Coinbase21798d9e740a69…e6537a6e41070b
1 in β†’ 1 out10.1500 XPM109 B
AdaUfNWz…3GgD9yxT
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.

1.272 Γ— 10⁹⁢(97-digit number)
12727981744494419699…30445318980873010189
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
1.272 Γ— 10⁹⁢(97-digit number)
12727981744494419699…30445318980873010189
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.545 Γ— 10⁹⁢(97-digit number)
25455963488988839399…60890637961746020379
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.091 Γ— 10⁹⁢(97-digit number)
50911926977977678798…21781275923492040759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.018 Γ— 10⁹⁷(98-digit number)
10182385395595535759…43562551846984081519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.036 Γ— 10⁹⁷(98-digit number)
20364770791191071519…87125103693968163039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.072 Γ— 10⁹⁷(98-digit number)
40729541582382143038…74250207387936326079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.145 Γ— 10⁹⁷(98-digit number)
81459083164764286077…48500414775872652159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.629 Γ— 10⁹⁸(99-digit number)
16291816632952857215…97000829551745304319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.258 Γ— 10⁹⁸(99-digit number)
32583633265905714431…94001659103490608639
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
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