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Block #206,923

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/13/2013, 3:06:22 AM Β· Difficulty 9.9017 Β· 6,599,466 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fb5331ebdca9cd35ba98a69aebcd121a4fe312f23ec43113dd5b5b64d1d446c9
View on Chainz β†—

Height

#206,923

Difficulty

9.901739

Transactions

2

Size

686 B

Version

2

Bits

09e6d85c

Nonce

282,602

Timestamp

10/13/2013, 3:06:22 AM

Confirmations

6,599,466

Mined by

⛏️ P2SHAGD4ELPmV9VxECkLLRQiFxvMNQsYtybN6f

Merkle Root

73b53a47ce7d8fb1b9eb3a1818e2496c7761f96311d7bff4daeb86332d692a63
Transactions (2)
Coinbasedfedc50d4facd6…7f719134219411
1 in β†’ 1 out10.1900 XPM109 B
AGD4ELPm…sYtybN6f
b0721dac4254be…221a324b2f4b3d
3 in β†’ 1 out9.0044 XPM488 B
AZekc9vM…TkyD7EeC
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.

1.220 Γ— 10⁹³(94-digit number)
12209615341412540232…13422811980273089751
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
1.220 Γ— 10⁹³(94-digit number)
12209615341412540232…13422811980273089751
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.441 Γ— 10⁹³(94-digit number)
24419230682825080465…26845623960546179501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.883 Γ— 10⁹³(94-digit number)
48838461365650160930…53691247921092359001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.767 Γ— 10⁹³(94-digit number)
97676922731300321861…07382495842184718001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.953 Γ— 10⁹⁴(95-digit number)
19535384546260064372…14764991684369436001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.907 Γ— 10⁹⁴(95-digit number)
39070769092520128744…29529983368738872001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.814 Γ— 10⁹⁴(95-digit number)
78141538185040257489…59059966737477744001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.562 Γ— 10⁹⁡(96-digit number)
15628307637008051497…18119933474955488001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.125 Γ— 10⁹⁡(96-digit number)
31256615274016102995…36239866949910976001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,695,202 XPMΒ·at block #6,806,388 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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