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Block #334,521

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/29/2013, 1:48:41 PM Β· Difficulty 10.1562 Β· 6,460,062 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dfe7976a1a1f294fdd385e39e5ed5b766e595226904f36c8dfd4348703bb4bb6
View on Chainz β†—

Height

#334,521

Difficulty

10.156178

Transactions

2

Size

359 B

Version

2

Bits

0a27fb50

Nonce

15,581

Timestamp

12/29/2013, 1:48:41 PM

Confirmations

6,460,062

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

199655fa9bcafe8310c61bc72c831b3e7f0a3f3697f3e4ebb11ded9e14e16341
Transactions (2)
Coinbase39d3aa52caf606…e9de2412de9b16
1 in β†’ 1 out9.6900 XPM110 B
AeKNrjNj…1NEq95Ta
9ff7bcf9b74cff…0c99472d087681
1 in β†’ 1 out9.7400 XPM158 B
ATV4M1CV…dd9zw8nH
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.

8.688 Γ— 10⁹⁷(98-digit number)
86888187803014668290…84516789139842242399
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
8.688 Γ— 10⁹⁷(98-digit number)
86888187803014668290…84516789139842242399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.737 Γ— 10⁹⁸(99-digit number)
17377637560602933658…69033578279684484799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.475 Γ— 10⁹⁸(99-digit number)
34755275121205867316…38067156559368969599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.951 Γ— 10⁹⁸(99-digit number)
69510550242411734632…76134313118737939199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.390 Γ— 10⁹⁹(100-digit number)
13902110048482346926…52268626237475878399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.780 Γ— 10⁹⁹(100-digit number)
27804220096964693852…04537252474951756799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.560 Γ— 10⁹⁹(100-digit number)
55608440193929387705…09074504949903513599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.112 Γ— 10¹⁰⁰(101-digit number)
11121688038785877541…18149009899807027199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.224 Γ— 10¹⁰⁰(101-digit number)
22243376077571755082…36298019799614054399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.448 Γ— 10¹⁰⁰(101-digit number)
44486752155143510164…72596039599228108799
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:57,600,711 XPMΒ·at block #6,794,582 Β· updates every 60s
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