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Block #234,753

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/30/2013, 12:34:14 PM Β· Difficulty 9.9445 Β· 6,571,998 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
682f96752d06fb5416fb586f3cac9ec8a37b95f6b7a5a97ebfb4ea517be2fc05
View on Chainz β†—

Height

#234,753

Difficulty

9.944543

Transactions

2

Size

584 B

Version

2

Bits

09f1cd92

Nonce

105,493

Timestamp

10/30/2013, 12:34:14 PM

Confirmations

6,571,998

Mined by

⛏️ P2SHAWzjcy2amFZJGd4QnfQcp3N6ru2SoqWfVy

Merkle Root

1fc5030bef485915e8cb5491881bcef2899e2f9702818a038b8a5d885d229559
Transactions (2)
Coinbased14e5019ee06b9…15ecfed6cd4218
1 in β†’ 1 out10.1100 XPM109 B
AWzjcy2a…2SoqWfVy
3490ca14ca11bf…2579debb543359
3 in β†’ 1 out30.5500 XPM385 B
AMfUufeM…gqTpCamv
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.

7.413 Γ— 10⁹⁴(95-digit number)
74133338439702089690…54702953628278927359
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
7.413 Γ— 10⁹⁴(95-digit number)
74133338439702089690…54702953628278927359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.482 Γ— 10⁹⁡(96-digit number)
14826667687940417938…09405907256557854719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.965 Γ— 10⁹⁡(96-digit number)
29653335375880835876…18811814513115709439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.930 Γ— 10⁹⁡(96-digit number)
59306670751761671752…37623629026231418879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.186 Γ— 10⁹⁢(97-digit number)
11861334150352334350…75247258052462837759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.372 Γ— 10⁹⁢(97-digit number)
23722668300704668701…50494516104925675519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.744 Γ— 10⁹⁢(97-digit number)
47445336601409337402…00989032209851351039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.489 Γ— 10⁹⁢(97-digit number)
94890673202818674804…01978064419702702079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.897 Γ— 10⁹⁷(98-digit number)
18978134640563734960…03956128839405404159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.795 Γ— 10⁹⁷(98-digit number)
37956269281127469921…07912257678810808319
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:57,698,107 XPMΒ·at block #6,806,750 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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