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Block #2,271,143

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/28/2017, 1:38:10 AM Β· Difficulty 10.9534 Β· 4,571,983 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3003a21d656b49ea8faaf36c67e812226f23f00c006cc7cb3b2e100656c1a5f0
View on Chainz β†—

Height

#2,271,143

Difficulty

10.953441

Transactions

1

Size

201 B

Version

2

Bits

0af414b8

Nonce

1,630,037,877

Timestamp

8/28/2017, 1:38:10 AM

Confirmations

4,571,983

Mined by

⛏️ P2SHAbeZuRLR1mbo3YJHMdsDhBPdUsCkrB5coQ

Merkle Root

269ebc1fa79871f344ae3186a145a57d54e3088eebab81f3d8ec68d06bd8372f
Transactions (1)
Coinbase269ebc1fa79871…ec68d06bd8372f
1 in β†’ 1 out8.3200 XPM110 B
AbeZuRLR…CkrB5coQ
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.

2.796 Γ— 10⁹⁢(97-digit number)
27962263660877767115…69309519430175887361
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
2.796 Γ— 10⁹⁢(97-digit number)
27962263660877767115…69309519430175887361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.592 Γ— 10⁹⁢(97-digit number)
55924527321755534230…38619038860351774721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.118 Γ— 10⁹⁷(98-digit number)
11184905464351106846…77238077720703549441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.236 Γ— 10⁹⁷(98-digit number)
22369810928702213692…54476155441407098881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.473 Γ— 10⁹⁷(98-digit number)
44739621857404427384…08952310882814197761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.947 Γ— 10⁹⁷(98-digit number)
89479243714808854768…17904621765628395521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.789 Γ— 10⁹⁸(99-digit number)
17895848742961770953…35809243531256791041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.579 Γ— 10⁹⁸(99-digit number)
35791697485923541907…71618487062513582081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.158 Γ— 10⁹⁸(99-digit number)
71583394971847083814…43236974125027164161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.431 Γ— 10⁹⁹(100-digit number)
14316678994369416762…86473948250054328321
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:57,989,374 XPMΒ·at block #6,843,125 Β· updates every 60s
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