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Block #398,971

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/11/2014, 3:20:04 AM Β· Difficulty 10.4193 Β· 6,410,314 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
92c090634634cef707c61aa8de0b1b94ad48a2c7c73133738b36a48be9002d2e
View on Chainz β†—

Height

#398,971

Difficulty

10.419295

Transactions

1

Size

209 B

Version

2

Bits

0a6b56f0

Nonce

772,766

Timestamp

2/11/2014, 3:20:04 AM

Confirmations

6,410,314

Mined by

⛏️ P2SHAW6FdqAF2QFTdoj8WBd1FEKDKLmbtgXE2r

Merkle Root

df24e84779045ea3fe77e316b2573e0951a7e12120ab96284a766a7b82c6f0a4
Transactions (1)
Coinbasedf24e84779045e…766a7b82c6f0a4
1 in β†’ 1 out9.2000 XPM118 B
AW6FdqAF…mbtgXE2r
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.

5.491 Γ— 10⁹⁢(97-digit number)
54913085435764495307…41542927235338630241
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
5.491 Γ— 10⁹⁢(97-digit number)
54913085435764495307…41542927235338630241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.098 Γ— 10⁹⁷(98-digit number)
10982617087152899061…83085854470677260481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.196 Γ— 10⁹⁷(98-digit number)
21965234174305798122…66171708941354520961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.393 Γ— 10⁹⁷(98-digit number)
43930468348611596245…32343417882709041921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.786 Γ— 10⁹⁷(98-digit number)
87860936697223192491…64686835765418083841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.757 Γ— 10⁹⁸(99-digit number)
17572187339444638498…29373671530836167681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.514 Γ— 10⁹⁸(99-digit number)
35144374678889276996…58747343061672335361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.028 Γ— 10⁹⁸(99-digit number)
70288749357778553993…17494686123344670721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.405 Γ— 10⁹⁹(100-digit number)
14057749871555710798…34989372246689341441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.811 Γ— 10⁹⁹(100-digit number)
28115499743111421597…69978744493378682881
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:57,718,350 XPMΒ·at block #6,809,284 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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