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Block #2,173,372

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/23/2017, 7:05:05 AM Β· Difficulty 10.9097 Β· 4,657,386 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
246336e3bdb81eb964f60cbd10199875932bbe0f6530b696dbd28401b46b0851
View on Chainz β†—

Height

#2,173,372

Difficulty

10.909699

Transactions

1

Size

209 B

Version

2

Bits

0ae8e209

Nonce

89,388,116

Timestamp

6/23/2017, 7:05:05 AM

Confirmations

4,657,386

Mined by

⛏️ P2SHAM6GYpjwZFjhLNzHZAfmRp8jwiaw86QDtR

Merkle Root

685c6e5ce98ca2639b1edddda5373ed025784e21cdcc9c273d63c069ff507acd
Transactions (1)
Coinbase685c6e5ce98ca2…63c069ff507acd
1 in β†’ 1 out8.3900 XPM118 B
AM6GYpjw…aw86QDtR
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.

9.550 Γ— 10⁹⁢(97-digit number)
95503724652791879661…46771564438788266241
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
9.550 Γ— 10⁹⁢(97-digit number)
95503724652791879661…46771564438788266241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.910 Γ— 10⁹⁷(98-digit number)
19100744930558375932…93543128877576532481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.820 Γ— 10⁹⁷(98-digit number)
38201489861116751864…87086257755153064961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.640 Γ— 10⁹⁷(98-digit number)
76402979722233503729…74172515510306129921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.528 Γ— 10⁹⁸(99-digit number)
15280595944446700745…48345031020612259841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.056 Γ— 10⁹⁸(99-digit number)
30561191888893401491…96690062041224519681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.112 Γ— 10⁹⁸(99-digit number)
61122383777786802983…93380124082449039361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.222 Γ— 10⁹⁹(100-digit number)
12224476755557360596…86760248164898078721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.444 Γ— 10⁹⁹(100-digit number)
24448953511114721193…73520496329796157441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.889 Γ— 10⁹⁹(100-digit number)
48897907022229442386…47040992659592314881
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:57,890,201 XPMΒ·at block #6,830,757 Β· updates every 60s
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