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Block #273,638

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/25/2013, 9:51:48 PM Β· Difficulty 9.9554 Β· 6,536,617 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
93d263214c0eb9339e35acdda680dc93654eab249065d718672d46f4ca25acaf
View on Chainz β†—

Height

#273,638

Difficulty

9.955369

Transactions

2

Size

1018 B

Version

2

Bits

09f49311

Nonce

737

Timestamp

11/25/2013, 9:51:48 PM

Confirmations

6,536,617

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

63cc1b073e24f97116f15aebf268fd4ac5e420504bda3a6645455b5cd5b2b101
Transactions (2)
Coinbase51e27bb17b93e2…2da46a3711d1c1
1 in β†’ 1 out10.0800 XPM110 B
AeKNrjNj…1NEq95Ta
ff753dbdae4ac4…42f07be03827d6
5 in β†’ 2 out573.8583 XPM819 B
AV1XaCWZ…2ZTgHVdWAR1QCMdG…5QmwQnuS
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.

2.580 Γ— 10⁹³(94-digit number)
25802459620510679580…66747632796846834079
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.580 Γ— 10⁹³(94-digit number)
25802459620510679580…66747632796846834079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.160 Γ— 10⁹³(94-digit number)
51604919241021359161…33495265593693668159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.032 Γ— 10⁹⁴(95-digit number)
10320983848204271832…66990531187387336319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.064 Γ— 10⁹⁴(95-digit number)
20641967696408543664…33981062374774672639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.128 Γ— 10⁹⁴(95-digit number)
41283935392817087328…67962124749549345279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.256 Γ— 10⁹⁴(95-digit number)
82567870785634174657…35924249499098690559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.651 Γ— 10⁹⁡(96-digit number)
16513574157126834931…71848498998197381119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.302 Γ— 10⁹⁡(96-digit number)
33027148314253669863…43696997996394762239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.605 Γ— 10⁹⁡(96-digit number)
66054296628507339726…87393995992789524479
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,726,113 XPMΒ·at block #6,810,254 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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