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Block #138,066

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/28/2013, 4:52:45 AM Β· Difficulty 9.8241 Β· 6,677,990 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e243b8095819b2d99614fe2252c0a69ee9b2c5b70e63f4e2a69ca24e98a0f1d3
View on Chainz β†—

Height

#138,066

Difficulty

9.824085

Transactions

2

Size

539 B

Version

2

Bits

09d2f741

Nonce

92,029

Timestamp

8/28/2013, 4:52:45 AM

Confirmations

6,677,990

Mined by

⛏️ P2SHAVgUWtFMMnXoPAA3RMmMmK9jsw6WVuTQK9

Merkle Root

c8593eccf63e785ed64fe69a700c46ccfb97779216fdb125a2d12fe99eeb7d36
Transactions (2)
Coinbaseed2a9cbc0fa372…5f7f2bc3d6d507
1 in β†’ 1 out10.3600 XPM109 B
AVgUWtFM…6WVuTQK9
c45a1cd3586d73…d50873d523b46e
2 in β†’ 1 out181.9900 XPM340 B
AWD4VgHE…qxX9q4vi
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.

1.559 Γ— 10⁹⁡(96-digit number)
15591851809070428787…00906986431536074239
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
1.559 Γ— 10⁹⁡(96-digit number)
15591851809070428787…00906986431536074239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.118 Γ— 10⁹⁡(96-digit number)
31183703618140857574…01813972863072148479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.236 Γ— 10⁹⁡(96-digit number)
62367407236281715148…03627945726144296959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.247 Γ— 10⁹⁢(97-digit number)
12473481447256343029…07255891452288593919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.494 Γ— 10⁹⁢(97-digit number)
24946962894512686059…14511782904577187839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.989 Γ— 10⁹⁢(97-digit number)
49893925789025372118…29023565809154375679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.978 Γ— 10⁹⁢(97-digit number)
99787851578050744237…58047131618308751359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.995 Γ— 10⁹⁷(98-digit number)
19957570315610148847…16094263236617502719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.991 Γ— 10⁹⁷(98-digit number)
39915140631220297694…32188526473235005439
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:57,772,563 XPMΒ·at block #6,816,055 Β· updates every 60s
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