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Block #113,616

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/12/2013, 3:40:57 PM Β· Difficulty 9.7340 Β· 6,713,148 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9c4ea2aea00a5f8f51a95ac73131e10974fb338c1c7f0e250b61abdde9d736ac
View on Chainz β†—

Height

#113,616

Difficulty

9.733980

Transactions

1

Size

200 B

Version

2

Bits

09bbe617

Nonce

648,271

Timestamp

8/12/2013, 3:40:57 PM

Confirmations

6,713,148

Mined by

⛏️ P2SHAGELmJR6aPRjt3Z8ALYc9YsGpGUuQ4Rhjr

Merkle Root

7c8f71f9e47d384df1d5a89c495080c538fc740a36e9c35569313d8801a85ec7
Transactions (1)
Coinbase7c8f71f9e47d38…313d8801a85ec7
1 in β†’ 1 out10.5400 XPM109 B
AGELmJR6…UuQ4Rhjr
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.

2.781 Γ— 10⁹⁢(97-digit number)
27817950151664888286…07718305782566474079
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
2.781 Γ— 10⁹⁢(97-digit number)
27817950151664888286…07718305782566474079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.563 Γ— 10⁹⁢(97-digit number)
55635900303329776572…15436611565132948159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.112 Γ— 10⁹⁷(98-digit number)
11127180060665955314…30873223130265896319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.225 Γ— 10⁹⁷(98-digit number)
22254360121331910628…61746446260531792639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.450 Γ— 10⁹⁷(98-digit number)
44508720242663821257…23492892521063585279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.901 Γ— 10⁹⁷(98-digit number)
89017440485327642515…46985785042127170559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.780 Γ— 10⁹⁸(99-digit number)
17803488097065528503…93971570084254341119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.560 Γ— 10⁹⁸(99-digit number)
35606976194131057006…87943140168508682239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.121 Γ— 10⁹⁸(99-digit number)
71213952388262114012…75886280337017364479
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:57,858,272 XPMΒ·at block #6,826,763 Β· updates every 60s
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