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Block #154,208

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/7/2013, 12:29:20 PM Β· Difficulty 9.8643 Β· 6,654,739 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a90e59f2729eaede1e810c0bd179ea98f1cce8efaec3475465cbdda2022ea6cf
View on Chainz β†—

Height

#154,208

Difficulty

9.864267

Transactions

1

Size

200 B

Version

2

Bits

09dd409f

Nonce

40,129

Timestamp

9/7/2013, 12:29:20 PM

Confirmations

6,654,739

Mined by

⛏️ P2SHANNP26d7MpgaTviL4gpx3seETjc8ABLJ7e

Merkle Root

36ef9eb6aaac21913aa110aa0868b3a1b9fbf73dfd8cf6d4bbb5362c1398d1a6
Transactions (1)
Coinbase36ef9eb6aaac21…b5362c1398d1a6
1 in β†’ 1 out10.2600 XPM109 B
ANNP26d7…c8ABLJ7e
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.

1.667 Γ— 10⁹⁢(97-digit number)
16678840429427310075…79008972956919985439
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
1.667 Γ— 10⁹⁢(97-digit number)
16678840429427310075…79008972956919985439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.335 Γ— 10⁹⁢(97-digit number)
33357680858854620150…58017945913839970879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.671 Γ— 10⁹⁢(97-digit number)
66715361717709240300…16035891827679941759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.334 Γ— 10⁹⁷(98-digit number)
13343072343541848060…32071783655359883519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.668 Γ— 10⁹⁷(98-digit number)
26686144687083696120…64143567310719767039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.337 Γ— 10⁹⁷(98-digit number)
53372289374167392240…28287134621439534079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.067 Γ— 10⁹⁸(99-digit number)
10674457874833478448…56574269242879068159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.134 Γ— 10⁹⁸(99-digit number)
21348915749666956896…13148538485758136319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.269 Γ— 10⁹⁸(99-digit number)
42697831499333913792…26297076971516272639
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:57,715,635 XPMΒ·at block #6,808,946 Β· updates every 60s
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