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Block #2,097,900

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/3/2017, 2:27:40 AM Β· Difficulty 10.8691 Β· 4,726,598 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ff3cc52b90f04e8e52548805c086a73e916de3a0751ca7752a22a04fab271b99
View on Chainz β†—

Height

#2,097,900

Difficulty

10.869068

Transactions

2

Size

29.29 KB

Version

2

Bits

0ade7b36

Nonce

1,408,233,900

Timestamp

5/3/2017, 2:27:40 AM

Confirmations

4,726,598

Mined by

⛏️ P2SHAUEjdKrHuqG58peUXX5RyZu4Z2saoR2t76

Merkle Root

ed3086b964a69b955bce5cce74a28ebc37c6e1923c5ebefcb632d95c6257974c
Transactions (2)
Coinbase6df0538b698dfa…5339da03346ebe
1 in β†’ 1 out8.7500 XPM109 B
AUEjdKrH…saoR2t76
26ea55c6a3dba9…c146d1390c282d
201 in β†’ 1 out6.0000 XPM29.10 KB
AVaj27ki…Ntfy4Rjn
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.

4.564 Γ— 10⁹⁴(95-digit number)
45647549812339050483…17764479712788134401
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
4.564 Γ— 10⁹⁴(95-digit number)
45647549812339050483…17764479712788134401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.129 Γ— 10⁹⁴(95-digit number)
91295099624678100966…35528959425576268801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.825 Γ— 10⁹⁡(96-digit number)
18259019924935620193…71057918851152537601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.651 Γ— 10⁹⁡(96-digit number)
36518039849871240386…42115837702305075201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.303 Γ— 10⁹⁡(96-digit number)
73036079699742480773…84231675404610150401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.460 Γ— 10⁹⁢(97-digit number)
14607215939948496154…68463350809220300801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.921 Γ— 10⁹⁢(97-digit number)
29214431879896992309…36926701618440601601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.842 Γ— 10⁹⁢(97-digit number)
58428863759793984618…73853403236881203201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.168 Γ— 10⁹⁷(98-digit number)
11685772751958796923…47706806473762406401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.337 Γ— 10⁹⁷(98-digit number)
23371545503917593847…95413612947524812801
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:57,840,057 XPMΒ·at block #6,824,497 Β· updates every 60s
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