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Block #206,925

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/13/2013, 3:07:35 AM Β· Difficulty 9.9017 Β· 6,603,822 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
de65c44af2bee06fa29caa4928deaa09f88b6696871798e468e9fd13cb13cf92
View on Chainz β†—

Height

#206,925

Difficulty

9.901745

Transactions

1

Size

200 B

Version

2

Bits

09e6d8c5

Nonce

146,635

Timestamp

10/13/2013, 3:07:35 AM

Confirmations

6,603,822

Mined by

⛏️ P2SHAL2EWWZmctFoTxS7QgAsvUyr8tCwsD5iKb

Merkle Root

8ac04ff67f07b159e8b2c23b711ac158fcaac6264822acab05de5c37dc3a3fee
Transactions (1)
Coinbase8ac04ff67f07b1…de5c37dc3a3fee
1 in β†’ 1 out10.1800 XPM109 B
AL2EWWZm…CwsD5iKb
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.

1.405 Γ— 10⁹⁢(97-digit number)
14056364738503043017…01252630384704061441
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
1.405 Γ— 10⁹⁢(97-digit number)
14056364738503043017…01252630384704061441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.811 Γ— 10⁹⁢(97-digit number)
28112729477006086034…02505260769408122881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.622 Γ— 10⁹⁢(97-digit number)
56225458954012172069…05010521538816245761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.124 Γ— 10⁹⁷(98-digit number)
11245091790802434413…10021043077632491521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.249 Γ— 10⁹⁷(98-digit number)
22490183581604868827…20042086155264983041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.498 Γ— 10⁹⁷(98-digit number)
44980367163209737655…40084172310529966081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.996 Γ— 10⁹⁷(98-digit number)
89960734326419475311…80168344621059932161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.799 Γ— 10⁹⁸(99-digit number)
17992146865283895062…60336689242119864321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.598 Γ— 10⁹⁸(99-digit number)
35984293730567790124…20673378484239728641
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:57,730,068 XPMΒ·at block #6,810,746 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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