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Block #2,121,526

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/18/2017, 1:53:49 AM Β· Difficulty 10.9136 Β· 4,709,447 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3fb8001f4d9d42d74ce1e6e247e89d2a93ff4d1d96835cb8a4b0a6742e88954a
View on Chainz β†—

Height

#2,121,526

Difficulty

10.913606

Transactions

1

Size

200 B

Version

2

Bits

0ae9e21a

Nonce

997,755,431

Timestamp

5/18/2017, 1:53:49 AM

Confirmations

4,709,447

Mined by

⛏️ P2SHAS2JL8zKMq7Uf4uycBy4L98xkiv6LnMNCP

Merkle Root

b55abd775b8966068851b7a098c43ab0e05097fc4b5d1d4b1f3528ebc80613cd
Transactions (1)
Coinbaseb55abd775b8966…3528ebc80613cd
1 in β†’ 1 out8.3800 XPM110 B
AS2JL8zK…v6LnMNCP
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.

3.202 Γ— 10⁹⁡(96-digit number)
32028727948856859949…63597164565715425281
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
3.202 Γ— 10⁹⁡(96-digit number)
32028727948856859949…63597164565715425281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.405 Γ— 10⁹⁡(96-digit number)
64057455897713719898…27194329131430850561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.281 Γ— 10⁹⁢(97-digit number)
12811491179542743979…54388658262861701121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.562 Γ— 10⁹⁢(97-digit number)
25622982359085487959…08777316525723402241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.124 Γ— 10⁹⁢(97-digit number)
51245964718170975918…17554633051446804481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.024 Γ— 10⁹⁷(98-digit number)
10249192943634195183…35109266102893608961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.049 Γ— 10⁹⁷(98-digit number)
20498385887268390367…70218532205787217921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.099 Γ— 10⁹⁷(98-digit number)
40996771774536780734…40437064411574435841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.199 Γ— 10⁹⁷(98-digit number)
81993543549073561469…80874128823148871681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.639 Γ— 10⁹⁸(99-digit number)
16398708709814712293…61748257646297743361
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:57,891,923 XPMΒ·at block #6,830,972 Β· updates every 60s
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