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Block #101,360

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/6/2013, 2:46:17 PM Β· Difficulty 9.4588 Β· 6,725,398 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fcfbc078cda61f06d476f150f9c60a861e1ba391e6aa684c3dfedccd32a5d664
View on Chainz β†—

Height

#101,360

Difficulty

9.458803

Transactions

1

Size

200 B

Version

2

Bits

0975741b

Nonce

268,521

Timestamp

8/6/2013, 2:46:17 PM

Confirmations

6,725,398

Mined by

⛏️ P2SHAdDLcbs3wHYjSo3LWBo5FqDZdQ7WeS2vPx

Merkle Root

92eb80f57452423e1e89518bcf85b1a445acf80ca6af059c2bab61859ef68412
Transactions (1)
Coinbase92eb80f5745242…ab61859ef68412
1 in β†’ 1 out11.1600 XPM109 B
AdDLcbs3…7WeS2vPx
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.

5.900 Γ— 10⁹⁢(97-digit number)
59002962074123793056…60489121757521576719
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
5.900 Γ— 10⁹⁢(97-digit number)
59002962074123793056…60489121757521576719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.180 Γ— 10⁹⁷(98-digit number)
11800592414824758611…20978243515043153439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.360 Γ— 10⁹⁷(98-digit number)
23601184829649517222…41956487030086306879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.720 Γ— 10⁹⁷(98-digit number)
47202369659299034445…83912974060172613759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.440 Γ— 10⁹⁷(98-digit number)
94404739318598068890…67825948120345227519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.888 Γ— 10⁹⁸(99-digit number)
18880947863719613778…35651896240690455039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.776 Γ— 10⁹⁸(99-digit number)
37761895727439227556…71303792481380910079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.552 Γ— 10⁹⁸(99-digit number)
75523791454878455112…42607584962761820159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.510 Γ— 10⁹⁹(100-digit number)
15104758290975691022…85215169925523640319
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
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