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Block #789,209

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/30/2014, 9:12:47 AM Β· Difficulty 10.9740 Β· 6,023,658 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
30364d9b7c0000206498360aed702cd8f043b057c43d3fcbb89f1555c17f923a
View on Chainz β†—

Height

#789,209

Difficulty

10.974039

Transactions

1

Size

242 B

Version

2

Bits

0af95a97

Nonce

124,193,520

Timestamp

10/30/2014, 9:12:47 AM

Confirmations

6,023,658

Mined by

⛏️ P2SHAYFivgcJEqUfH1zEbfNs35USz3FT8wELGF

Merkle Root

2c97eacd5871ea75b6663093a26ddc02d2a54ccf8516c37ee1307a8a783c86f1
Transactions (1)
Coinbase2c97eacd5871ea…307a8a783c86f1
1 in β†’ 2 out8.2900 XPM152 B
AYFivgcJ…FT8wELGFALPu3s2c…EJXLjVFh
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.

2.575 Γ— 10⁹⁡(96-digit number)
25750262540230148097…36594961177925416001
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.575 Γ— 10⁹⁡(96-digit number)
25750262540230148097…36594961177925416001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.150 Γ— 10⁹⁡(96-digit number)
51500525080460296195…73189922355850832001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.030 Γ— 10⁹⁢(97-digit number)
10300105016092059239…46379844711701664001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.060 Γ— 10⁹⁢(97-digit number)
20600210032184118478…92759689423403328001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.120 Γ— 10⁹⁢(97-digit number)
41200420064368236956…85519378846806656001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.240 Γ— 10⁹⁢(97-digit number)
82400840128736473912…71038757693613312001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.648 Γ— 10⁹⁷(98-digit number)
16480168025747294782…42077515387226624001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.296 Γ— 10⁹⁷(98-digit number)
32960336051494589565…84155030774453248001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.592 Γ— 10⁹⁷(98-digit number)
65920672102989179130…68310061548906496001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.318 Γ— 10⁹⁸(99-digit number)
13184134420597835826…36620123097812992001
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,746,965 XPMΒ·at block #6,812,866 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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