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Block #151,147

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/5/2013, 12:13:46 PM Β· Difficulty 9.8597 Β· 6,644,190 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c61e8af4756851cfb6140e65013774030cf210348d3dc7b75e7baa0eb4ca6f4b
View on Chainz β†—

Height

#151,147

Difficulty

9.859695

Transactions

2

Size

422 B

Version

2

Bits

09dc14fa

Nonce

169,945

Timestamp

9/5/2013, 12:13:46 PM

Confirmations

6,644,190

Mined by

⛏️ P2SHAKhaGKFX4s17sd56QzVFtsa8mSKjeAXtBv

Merkle Root

1800a1f9c720e4aa71787336f549d7bb202f65abc2997b982dcc5a15325d93f5
Transactions (2)
Coinbase0f75b9a27cc926…6027c3db6530c3
1 in β†’ 1 out10.2800 XPM109 B
AKhaGKFX…KjeAXtBv
d4afffccb7da53…188607a4f9d988
1 in β†’ 2 out6.1254 XPM226 B
APJ1iDR4…4AnDpBFWAQAph9Ee…Bh4omZLF
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.

6.005 Γ— 10⁸⁢(87-digit number)
60058465798719746745…69573528416871317019
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
6.005 Γ— 10⁸⁢(87-digit number)
60058465798719746745…69573528416871317019
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.201 Γ— 10⁸⁷(88-digit number)
12011693159743949349…39147056833742634039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.402 Γ— 10⁸⁷(88-digit number)
24023386319487898698…78294113667485268079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.804 Γ— 10⁸⁷(88-digit number)
48046772638975797396…56588227334970536159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.609 Γ— 10⁸⁷(88-digit number)
96093545277951594792…13176454669941072319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.921 Γ— 10⁸⁸(89-digit number)
19218709055590318958…26352909339882144639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.843 Γ— 10⁸⁸(89-digit number)
38437418111180637916…52705818679764289279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.687 Γ— 10⁸⁸(89-digit number)
76874836222361275833…05411637359528578559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.537 Γ— 10⁸⁹(90-digit number)
15374967244472255166…10823274719057157119
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:57,606,755 XPMΒ·at block #6,795,336 Β· updates every 60s
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