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Block #156,321

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/8/2013, 9:08:44 PM Β· Difficulty 9.8684 Β· 6,670,990 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
71b59f3e4c65dcabbdeeb1b37c84db7144b4a5add1bea3227591a7181cbd62f7
View on Chainz β†—

Height

#156,321

Difficulty

9.868417

Transactions

1

Size

199 B

Version

2

Bits

09de5098

Nonce

188,963

Timestamp

9/8/2013, 9:08:44 PM

Confirmations

6,670,990

Mined by

⛏️ P2SHAetpQsvWbRdpVzLR1MmQMvbogyBEePeKKm

Merkle Root

68e2cd825842703361b24084a2f04e2ee9b2c20d8ad2171cecbd48f283a7195d
Transactions (1)
Coinbase68e2cd82584270…bd48f283a7195d
1 in β†’ 1 out10.2500 XPM109 B
AetpQsvW…BEePeKKm
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.

8.391 Γ— 10⁹⁴(95-digit number)
83912314696770575853…01817605484214039999
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
8.391 Γ— 10⁹⁴(95-digit number)
83912314696770575853…01817605484214039999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.678 Γ— 10⁹⁡(96-digit number)
16782462939354115170…03635210968428079999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.356 Γ— 10⁹⁡(96-digit number)
33564925878708230341…07270421936856159999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.712 Γ— 10⁹⁡(96-digit number)
67129851757416460682…14540843873712319999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.342 Γ— 10⁹⁢(97-digit number)
13425970351483292136…29081687747424639999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.685 Γ— 10⁹⁢(97-digit number)
26851940702966584273…58163375494849279999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.370 Γ— 10⁹⁢(97-digit number)
53703881405933168546…16326750989698559999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.074 Γ— 10⁹⁷(98-digit number)
10740776281186633709…32653501979397119999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.148 Γ— 10⁹⁷(98-digit number)
21481552562373267418…65307003958794239999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.296 Γ— 10⁹⁷(98-digit number)
42963105124746534836…30614007917588479999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,862,600 XPMΒ·at block #6,827,310 Β· updates every 60s
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