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Block #1,490,885

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/10/2016, 7:13:18 AM Β· Difficulty 10.6851 Β· 5,334,668 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f97dd86d13658f974538fc10a390aad0987437a68143042c5a48aef9e7c2eb5a
View on Chainz β†—

Height

#1,490,885

Difficulty

10.685098

Transactions

2

Size

14.29 KB

Version

2

Bits

0aaf628d

Nonce

120,847,170

Timestamp

3/10/2016, 7:13:18 AM

Confirmations

5,334,668

Mined by

⛏️ P2SHAex5FJ959CPyz9ehaeuthVRjontFB5GtwW

Merkle Root

32fffc12c11249b574bbffb6189185cf659aeca9d0f5fbc352295b8f6b6f0080
Transactions (2)
Coinbase188eac87347f82…677f517f60f377
1 in β†’ 1 out8.9100 XPM110 B
Aex5FJ95…tFB5GtwW
eeda6885258c3e…e76ae4cab2e48d
97 in β†’ 2 out206.5780 XPM14.09 KB
AZLEZw1d…yWWSAHDgAQHE5e6H…xDwU3vYU
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.

4.020 Γ— 10⁹³(94-digit number)
40200201852693918542…04409856552419941401
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
4.020 Γ— 10⁹³(94-digit number)
40200201852693918542…04409856552419941401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.040 Γ— 10⁹³(94-digit number)
80400403705387837084…08819713104839882801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.608 Γ— 10⁹⁴(95-digit number)
16080080741077567416…17639426209679765601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.216 Γ— 10⁹⁴(95-digit number)
32160161482155134833…35278852419359531201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.432 Γ— 10⁹⁴(95-digit number)
64320322964310269667…70557704838719062401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.286 Γ— 10⁹⁡(96-digit number)
12864064592862053933…41115409677438124801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.572 Γ— 10⁹⁡(96-digit number)
25728129185724107867…82230819354876249601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.145 Γ— 10⁹⁡(96-digit number)
51456258371448215734…64461638709752499201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.029 Γ— 10⁹⁢(97-digit number)
10291251674289643146…28923277419504998401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.058 Γ— 10⁹⁢(97-digit number)
20582503348579286293…57846554839009996801
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:57,848,525 XPMΒ·at block #6,825,552 Β· updates every 60s
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