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Block #54,106

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/16/2013, 6:42:54 PM Β· Difficulty 8.9303 Β· 6,763,306 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
69d8f2f6099177479618da518d399c12adcad6f36a14db699c36c40af92c0cca
View on Chainz β†—

Height

#54,106

Difficulty

8.930302

Transactions

1

Size

197 B

Version

2

Bits

08ee283e

Nonce

56

Timestamp

7/16/2013, 6:42:54 PM

Confirmations

6,763,306

Mined by

⛏️ P2SHAcuRhoVunZmd7TM7Neh2VRFvWv6Pu86km9

Merkle Root

7affede43c700563f63cdb296f3d0ceb5e7f0d97cb3e2978b38e2cd6fbfad9dd
Transactions (1)
Coinbase7affede43c7005…8e2cd6fbfad9dd
1 in β†’ 1 out12.5200 XPM110 B
AcuRhoVu…6Pu86km9
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.

3.157 Γ— 10⁸⁢(87-digit number)
31578423948452276824…13423998471058597679
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
3.157 Γ— 10⁸⁢(87-digit number)
31578423948452276824…13423998471058597679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.315 Γ— 10⁸⁢(87-digit number)
63156847896904553648…26847996942117195359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.263 Γ— 10⁸⁷(88-digit number)
12631369579380910729…53695993884234390719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.526 Γ— 10⁸⁷(88-digit number)
25262739158761821459…07391987768468781439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.052 Γ— 10⁸⁷(88-digit number)
50525478317523642918…14783975536937562879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.010 Γ— 10⁸⁸(89-digit number)
10105095663504728583…29567951073875125759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.021 Γ— 10⁸⁸(89-digit number)
20210191327009457167…59135902147750251519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.042 Γ— 10⁸⁸(89-digit number)
40420382654018914335…18271804295500503039
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8

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
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