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Block #2,150,167

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/7/2017, 1:22:58 PM Β· Difficulty 10.8987 Β· 4,692,729 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
75714f1741d1e5f5aec5d94de41f0c3e790ef9922179ab354847b01821f582dd
View on Chainz β†—

Height

#2,150,167

Difficulty

10.898703

Transactions

2

Size

425 B

Version

2

Bits

0ae6116c

Nonce

166,986,010

Timestamp

6/7/2017, 1:22:58 PM

Confirmations

4,692,729

Mined by

⛏️ P2SHAHoN5oy8yqP3LB3PdhD4Zarad6ZCkQRQij

Merkle Root

3e3d554b3a3e1ea91ffeca899962f76ea7b1e0b1ca93a375510b69a8e658784b
Transactions (2)
Coinbase201611b1a47087…11868561e4b85b
1 in β†’ 1 out8.4200 XPM109 B
AHoN5oy8…ZCkQRQij
e2519f4f8fe936…4563471754867b
1 in β†’ 2 out4176.4614 XPM227 B
AWXjMCT3…jf6SrAp1AV6GVuy1…YKkdVbyz
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.

7.891 Γ— 10⁹²(93-digit number)
78912258818330190779…74895312239749599999
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
7.891 Γ— 10⁹²(93-digit number)
78912258818330190779…74895312239749599999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.578 Γ— 10⁹³(94-digit number)
15782451763666038155…49790624479499199999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.156 Γ— 10⁹³(94-digit number)
31564903527332076311…99581248958998399999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.312 Γ— 10⁹³(94-digit number)
63129807054664152623…99162497917996799999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.262 Γ— 10⁹⁴(95-digit number)
12625961410932830524…98324995835993599999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.525 Γ— 10⁹⁴(95-digit number)
25251922821865661049…96649991671987199999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.050 Γ— 10⁹⁴(95-digit number)
50503845643731322099…93299983343974399999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.010 Γ— 10⁹⁡(96-digit number)
10100769128746264419…86599966687948799999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.020 Γ— 10⁹⁡(96-digit number)
20201538257492528839…73199933375897599999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.040 Γ— 10⁹⁡(96-digit number)
40403076514985057679…46399866751795199999
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,987,516 XPMΒ·at block #6,842,895 Β· updates every 60s
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