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Block #140,844

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/29/2013, 10:17:27 PM Β· Difficulty 9.8341 Β· 6,666,370 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7965a0df0d53c1508a828ad26c26256824d2a97e6a0e9f229391bed776e36a7b
View on Chainz β†—

Height

#140,844

Difficulty

9.834073

Transactions

1

Size

200 B

Version

2

Bits

09d585d4

Nonce

5,603

Timestamp

8/29/2013, 10:17:27 PM

Confirmations

6,666,370

Mined by

⛏️ P2SHAL2EWWZmctFoTxS7QgAsvUyr8tCwsD5iKb

Merkle Root

db07b177e1ca2c203fde0ea423ebb4143910e623318fe0a57e71f97f1b5923f1
Transactions (1)
Coinbasedb07b177e1ca2c…71f97f1b5923f1
1 in β†’ 1 out10.3200 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.

3.707 Γ— 10⁹⁢(97-digit number)
37071976639968320733…78435302153096460761
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
3.707 Γ— 10⁹⁢(97-digit number)
37071976639968320733…78435302153096460761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.414 Γ— 10⁹⁢(97-digit number)
74143953279936641467…56870604306192921521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.482 Γ— 10⁹⁷(98-digit number)
14828790655987328293…13741208612385843041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.965 Γ— 10⁹⁷(98-digit number)
29657581311974656587…27482417224771686081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.931 Γ— 10⁹⁷(98-digit number)
59315162623949313174…54964834449543372161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.186 Γ— 10⁹⁸(99-digit number)
11863032524789862634…09929668899086744321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.372 Γ— 10⁹⁸(99-digit number)
23726065049579725269…19859337798173488641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.745 Γ— 10⁹⁸(99-digit number)
47452130099159450539…39718675596346977281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.490 Γ— 10⁹⁸(99-digit number)
94904260198318901078…79437351192693954561
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:57,701,728 XPMΒ·at block #6,807,213 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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