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Block #1,501,996

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/18/2016, 11:09:12 AM Β· Difficulty 10.6424 Β· 5,330,974 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
03b9d9b7fc86d648ff301455ddf03deeb853e99c3c73d6a7bb3894460c0b52a7
View on Chainz β†—

Height

#1,501,996

Difficulty

10.642449

Transactions

1

Size

199 B

Version

2

Bits

0aa4778d

Nonce

629,294,417

Timestamp

3/18/2016, 11:09:12 AM

Confirmations

5,330,974

Mined by

⛏️ P2SHAS2obGuSZ2qmzDRoXcxnGiLdbM98dGXECH

Merkle Root

d1f3f9ddaf996c17adb9c7099e26d828f792e5a431182197dd8ac86536ad0bf7
Transactions (1)
Coinbased1f3f9ddaf996c…8ac86536ad0bf7
1 in β†’ 1 out8.8200 XPM109 B
AS2obGuS…98dGXECH
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.

4.549 Γ— 10⁹⁡(96-digit number)
45492899701782287231…38756695545435110401
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
4.549 Γ— 10⁹⁡(96-digit number)
45492899701782287231…38756695545435110401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.098 Γ— 10⁹⁡(96-digit number)
90985799403564574463…77513391090870220801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.819 Γ— 10⁹⁢(97-digit number)
18197159880712914892…55026782181740441601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.639 Γ— 10⁹⁢(97-digit number)
36394319761425829785…10053564363480883201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.278 Γ— 10⁹⁢(97-digit number)
72788639522851659571…20107128726961766401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.455 Γ— 10⁹⁷(98-digit number)
14557727904570331914…40214257453923532801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.911 Γ— 10⁹⁷(98-digit number)
29115455809140663828…80428514907847065601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.823 Γ— 10⁹⁷(98-digit number)
58230911618281327656…60857029815694131201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.164 Γ— 10⁹⁸(99-digit number)
11646182323656265531…21714059631388262401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.329 Γ— 10⁹⁸(99-digit number)
23292364647312531062…43428119262776524801
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:57,907,939 XPMΒ·at block #6,832,969 Β· updates every 60s
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