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Block #485,907

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/11/2014, 8:11:26 AM Β· Difficulty 10.6147 Β· 6,356,858 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
20603bc461e66cc2ab44a84d44a0241190f39de96e392adff706af1b91dbd58d
View on Chainz β†—

Height

#485,907

Difficulty

10.614654

Transactions

1

Size

206 B

Version

2

Bits

0a9d59fe

Nonce

10,044,533

Timestamp

4/11/2014, 8:11:26 AM

Confirmations

6,356,858

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

47c3b9ffd16355d4781ae98f642a29341a1b059bbdbf08f24f21bced1c4c4347
Transactions (1)
Coinbase47c3b9ffd16355…21bced1c4c4347
1 in β†’ 1 out8.8600 XPM116 B
AbwWkWZt…kawDhufa
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.

1.218 Γ— 10⁹⁴(95-digit number)
12189956058846756438…25463894567305264721
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
1.218 Γ— 10⁹⁴(95-digit number)
12189956058846756438…25463894567305264721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.437 Γ— 10⁹⁴(95-digit number)
24379912117693512877…50927789134610529441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.875 Γ— 10⁹⁴(95-digit number)
48759824235387025754…01855578269221058881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.751 Γ— 10⁹⁴(95-digit number)
97519648470774051508…03711156538442117761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.950 Γ— 10⁹⁡(96-digit number)
19503929694154810301…07422313076884235521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.900 Γ— 10⁹⁡(96-digit number)
39007859388309620603…14844626153768471041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.801 Γ— 10⁹⁡(96-digit number)
78015718776619241206…29689252307536942081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.560 Γ— 10⁹⁢(97-digit number)
15603143755323848241…59378504615073884161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.120 Γ— 10⁹⁢(97-digit number)
31206287510647696482…18757009230147768321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.241 Γ— 10⁹⁢(97-digit number)
62412575021295392965…37514018460295536641
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:57,986,459 XPMΒ·at block #6,842,764 Β· updates every 60s
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