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Block #212,447

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/16/2013, 7:18:55 AM Β· Difficulty 9.9190 Β· 6,605,130 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
11b32b937b63eeb925a0e337a38e174e6af0fa0498549a1f7a18f59fdfba819a
View on Chainz β†—

Height

#212,447

Difficulty

9.918990

Transactions

1

Size

206 B

Version

2

Bits

09eb42e7

Nonce

10,229

Timestamp

10/16/2013, 7:18:55 AM

Confirmations

6,605,130

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

e4372e52b5f17015f1908ab8007a69e1a10d44e55c74972c9693a4f6c8acd647
Transactions (1)
Coinbasee4372e52b5f170…93a4f6c8acd647
1 in β†’ 1 out10.1500 XPM116 B
AcLBm5Z9…S683d7c3
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.

5.944 Γ— 10⁹⁴(95-digit number)
59448741882565232743…60234138478627551039
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
5.944 Γ— 10⁹⁴(95-digit number)
59448741882565232743…60234138478627551039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.188 Γ— 10⁹⁡(96-digit number)
11889748376513046548…20468276957255102079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.377 Γ— 10⁹⁡(96-digit number)
23779496753026093097…40936553914510204159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.755 Γ— 10⁹⁡(96-digit number)
47558993506052186195…81873107829020408319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.511 Γ— 10⁹⁡(96-digit number)
95117987012104372390…63746215658040816639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.902 Γ— 10⁹⁢(97-digit number)
19023597402420874478…27492431316081633279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.804 Γ— 10⁹⁢(97-digit number)
38047194804841748956…54984862632163266559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.609 Γ— 10⁹⁢(97-digit number)
76094389609683497912…09969725264326533119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.521 Γ— 10⁹⁷(98-digit number)
15218877921936699582…19939450528653066239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.043 Γ— 10⁹⁷(98-digit number)
30437755843873399164…39878901057306132479
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:57,784,668 XPMΒ·at block #6,817,576 Β· updates every 60s
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