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Block #53,223

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/16/2013, 2:17:43 PM Β· Difficulty 8.9212 Β· 6,753,766 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4c92829a65c5fd94b74ba8efb02a926ce0e4710fe3d7a002da169dc7c6821434
View on Chainz β†—

Height

#53,223

Difficulty

8.921175

Transactions

1

Size

200 B

Version

2

Bits

08ebd221

Nonce

1,193

Timestamp

7/16/2013, 2:17:43 PM

Confirmations

6,753,766

Mined by

⛏️ P2SHAGKMgFpQL9MDwNBWU46pd8c73Ay9gJPnXo

Merkle Root

79cb0c5fe7105f934f1cf67ad48198e37f06501e7edfc90f2bc13775a88d6bda
Transactions (1)
Coinbase79cb0c5fe7105f…c13775a88d6bda
1 in β†’ 1 out12.5500 XPM110 B
AGKMgFpQ…y9gJPnXo
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.

2.639 Γ— 10⁹³(94-digit number)
26390183338323881562…39225961465502993149
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
2.639 Γ— 10⁹³(94-digit number)
26390183338323881562…39225961465502993149
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.278 Γ— 10⁹³(94-digit number)
52780366676647763124…78451922931005986299
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.055 Γ— 10⁹⁴(95-digit number)
10556073335329552624…56903845862011972599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.111 Γ— 10⁹⁴(95-digit number)
21112146670659105249…13807691724023945199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.222 Γ— 10⁹⁴(95-digit number)
42224293341318210499…27615383448047890399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.444 Γ— 10⁹⁴(95-digit number)
84448586682636420998…55230766896095780799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.688 Γ— 10⁹⁡(96-digit number)
16889717336527284199…10461533792191561599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.377 Γ— 10⁹⁡(96-digit number)
33779434673054568399…20923067584383123199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.755 Γ— 10⁹⁡(96-digit number)
67558869346109136798…41846135168766246399
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:57,700,015 XPMΒ·at block #6,806,988 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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