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Block #232,868

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/29/2013, 9:26:23 AM Β· Difficulty 9.9416 Β· 6,566,670 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8a60253fe11b8963984ad616dfea2c40c1ad9f83694a8b0f18e31bfe9c63943f
View on Chainz β†—

Height

#232,868

Difficulty

9.941554

Transactions

1

Size

198 B

Version

2

Bits

09f109ae

Nonce

125,893

Timestamp

10/29/2013, 9:26:23 AM

Confirmations

6,566,670

Mined by

⛏️ P2SHAefNmfCCiMUgcSMoZqwmWZgc6ARj9JS3UM

Merkle Root

c485599d8ecd8bbbdd25890a81cdfd71ade4647ce06f0a0fdaf6fa64628215a5
Transactions (1)
Coinbasec485599d8ecd8b…f6fa64628215a5
1 in β†’ 1 out10.1000 XPM109 B
AefNmfCC…Rj9JS3UM
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.

1.259 Γ— 10⁹²(93-digit number)
12594908337186814376…38708336411778186959
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
1.259 Γ— 10⁹²(93-digit number)
12594908337186814376…38708336411778186959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.518 Γ— 10⁹²(93-digit number)
25189816674373628753…77416672823556373919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.037 Γ— 10⁹²(93-digit number)
50379633348747257506…54833345647112747839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.007 Γ— 10⁹³(94-digit number)
10075926669749451501…09666691294225495679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.015 Γ— 10⁹³(94-digit number)
20151853339498903002…19333382588450991359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.030 Γ— 10⁹³(94-digit number)
40303706678997806005…38666765176901982719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.060 Γ— 10⁹³(94-digit number)
80607413357995612010…77333530353803965439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.612 Γ— 10⁹⁴(95-digit number)
16121482671599122402…54667060707607930879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.224 Γ— 10⁹⁴(95-digit number)
32242965343198244804…09334121415215861759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.448 Γ— 10⁹⁴(95-digit number)
64485930686396489608…18668242830431723519
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:57,640,355 XPMΒ·at block #6,799,537 Β· updates every 60s
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