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Block #151,251

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/5/2013, 1:42:06 PM Β· Difficulty 9.8602 Β· 6,653,912 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fcd93c0a97c07858283932c01fd48eafdd5ddec9d42cd0a5be55ff9c00062bc7
View on Chainz β†—

Height

#151,251

Difficulty

9.860166

Transactions

2

Size

1.79 KB

Version

2

Bits

09dc33d5

Nonce

302,859

Timestamp

9/5/2013, 1:42:06 PM

Confirmations

6,653,912

Mined by

⛏️ P2SHAVKorEuWzV5sVEonxKvsENVoqTjREVePkn

Merkle Root

9142d3d397bb2256ca70f2c77fa705f18c745fc925b92507238d655de68a707a
Transactions (2)
Coinbase09d70865bf549d…7e0e8e41e56603
1 in β†’ 1 out10.2900 XPM109 B
AVKorEuW…jREVePkn
18f4e3b0e45c23…5842adef9e0125
14 in β†’ 1 out144.0500 XPM1.60 KB
AJs27LEf…M76myr9t
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.

9.912 Γ— 10⁹⁴(95-digit number)
99122555518679929667…37700804922271973759
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
9.912 Γ— 10⁹⁴(95-digit number)
99122555518679929667…37700804922271973759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.982 Γ— 10⁹⁡(96-digit number)
19824511103735985933…75401609844543947519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.964 Γ— 10⁹⁡(96-digit number)
39649022207471971867…50803219689087895039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.929 Γ— 10⁹⁡(96-digit number)
79298044414943943734…01606439378175790079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.585 Γ— 10⁹⁢(97-digit number)
15859608882988788746…03212878756351580159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.171 Γ— 10⁹⁢(97-digit number)
31719217765977577493…06425757512703160319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.343 Γ— 10⁹⁢(97-digit number)
63438435531955154987…12851515025406320639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.268 Γ— 10⁹⁷(98-digit number)
12687687106391030997…25703030050812641279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.537 Γ— 10⁹⁷(98-digit number)
25375374212782061995…51406060101625282559
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:57,685,371 XPMΒ·at block #6,805,162 Β· updates every 60s
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