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Block #369,856

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/21/2014, 4:34:08 PM Β· Difficulty 10.4482 Β· 6,444,612 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3cb739a8a8a2c2a4189ab0163ae0671bfc78610e41b55b0653956cdf25d19bff
View on Chainz β†—

Height

#369,856

Difficulty

10.448215

Transactions

1

Size

221 B

Version

2

Bits

0a72be3e

Nonce

721,611

Timestamp

1/21/2014, 4:34:08 PM

Confirmations

6,444,612

Mined by

Ac2JYASPQD7vWBs42nkRqpCmFvtcBL5PEW

Merkle Root

690c73e6ce91707f33fcb97c744b015b5c6c71b756ca6c08b63ddf0b07d97853
Transactions (1)
Coinbase690c73e6ce9170…3ddf0b07d97853
1 in β†’ 2 out9.1500 XPM131 B
Ac2JYASP…tcBL5PEWAJno7LX2…vo4wdWtY
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.

3.950 Γ— 10⁹⁴(95-digit number)
39505405513359879335…26236248318064278881
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
3.950 Γ— 10⁹⁴(95-digit number)
39505405513359879335…26236248318064278881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.901 Γ— 10⁹⁴(95-digit number)
79010811026719758671…52472496636128557761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.580 Γ— 10⁹⁡(96-digit number)
15802162205343951734…04944993272257115521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.160 Γ— 10⁹⁡(96-digit number)
31604324410687903468…09889986544514231041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.320 Γ— 10⁹⁡(96-digit number)
63208648821375806936…19779973089028462081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.264 Γ— 10⁹⁢(97-digit number)
12641729764275161387…39559946178056924161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.528 Γ— 10⁹⁢(97-digit number)
25283459528550322774…79119892356113848321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.056 Γ— 10⁹⁢(97-digit number)
50566919057100645549…58239784712227696641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.011 Γ— 10⁹⁷(98-digit number)
10113383811420129109…16479569424455393281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.022 Γ— 10⁹⁷(98-digit number)
20226767622840258219…32959138848910786561
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:57,759,817 XPMΒ·at block #6,814,467 Β· updates every 60s
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