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Block #151,400

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/5/2013, 4:01:51 PM Β· Difficulty 9.8601 Β· 6,662,683 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
77643697a9584ef50c67deb6406e6f87fe55d913fe9e81f5d38b82f794c65e13
View on Chainz β†—

Height

#151,400

Difficulty

9.860140

Transactions

1

Size

199 B

Version

2

Bits

09dc3226

Nonce

37,478

Timestamp

9/5/2013, 4:01:51 PM

Confirmations

6,662,683

Mined by

⛏️ P2SHAdcZsTmngF3w7QDKZk3FhMgHUjW8T9Ht6R

Merkle Root

0c11a9c021fe588f6bd7e32b9371a78d3b8b27ce156936e7e6cde4d82e577804
Transactions (1)
Coinbase0c11a9c021fe58…cde4d82e577804
1 in β†’ 1 out10.2700 XPM109 B
AdcZsTmn…W8T9Ht6R
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.

6.342 Γ— 10⁹⁴(95-digit number)
63422553756829546720…48658607763247199999
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
6.342 Γ— 10⁹⁴(95-digit number)
63422553756829546720…48658607763247199999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.268 Γ— 10⁹⁡(96-digit number)
12684510751365909344…97317215526494399999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.536 Γ— 10⁹⁡(96-digit number)
25369021502731818688…94634431052988799999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.073 Γ— 10⁹⁡(96-digit number)
50738043005463637376…89268862105977599999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.014 Γ— 10⁹⁢(97-digit number)
10147608601092727475…78537724211955199999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.029 Γ— 10⁹⁢(97-digit number)
20295217202185454950…57075448423910399999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.059 Γ— 10⁹⁢(97-digit number)
40590434404370909901…14150896847820799999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.118 Γ— 10⁹⁢(97-digit number)
81180868808741819802…28301793695641599999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.623 Γ— 10⁹⁷(98-digit number)
16236173761748363960…56603587391283199999
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:57,756,745 XPMΒ·at block #6,814,082 Β· updates every 60s
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