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Block #340,977

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/3/2014, 4:02:18 AM Β· Difficulty 10.1320 Β· 6,463,921 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cdc1de4d5d182d6a3b0f869c408c54869acc71dd9d19005c66c8f29ae3aa56af
View on Chainz β†—

Height

#340,977

Difficulty

10.132009

Transactions

1

Size

205 B

Version

2

Bits

0a21cb5b

Nonce

240,825

Timestamp

1/3/2014, 4:02:18 AM

Confirmations

6,463,921

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

ed6ff5ba6aa5cab98d8766491634b7554595f445a8a255bcd24979911ad25f02
Transactions (1)
Coinbaseed6ff5ba6aa5ca…4979911ad25f02
1 in β†’ 1 out9.7300 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.

6.660 Γ— 10⁹²(93-digit number)
66609273763881384659…05183020764256438401
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
6.660 Γ— 10⁹²(93-digit number)
66609273763881384659…05183020764256438401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.332 Γ— 10⁹³(94-digit number)
13321854752776276931…10366041528512876801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.664 Γ— 10⁹³(94-digit number)
26643709505552553863…20732083057025753601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.328 Γ— 10⁹³(94-digit number)
53287419011105107727…41464166114051507201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.065 Γ— 10⁹⁴(95-digit number)
10657483802221021545…82928332228103014401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.131 Γ— 10⁹⁴(95-digit number)
21314967604442043091…65856664456206028801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.262 Γ— 10⁹⁴(95-digit number)
42629935208884086182…31713328912412057601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.525 Γ— 10⁹⁴(95-digit number)
85259870417768172364…63426657824824115201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.705 Γ— 10⁹⁡(96-digit number)
17051974083553634472…26853315649648230401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.410 Γ— 10⁹⁡(96-digit number)
34103948167107268945…53706631299296460801
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:57,683,255 XPMΒ·at block #6,804,897 Β· updates every 60s
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