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Block #28,817

1CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/13/2013, 1:29:59 PM Β· Difficulty 7.9830 Β· 6,770,538 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7bce9aea6d7345b76c2f049b82cda7e6bf5de3b9dd68c4d4bb589bcff476143a
View on Chainz β†—

Height

#28,817

Difficulty

7.983002

Transactions

1

Size

198 B

Version

2

Bits

07fba609

Nonce

452

Timestamp

7/13/2013, 1:29:59 PM

Confirmations

6,770,538

Mined by

⛏️ P2SHAWdtCUuJmNjYuej2P6C7RA2SGtHscHZriH

Merkle Root

48537c13fe4522ab8ce11c1e7d5ab56596ca57b26e18e2a8932df62cb27345af
Transactions (1)
Coinbase48537c13fe4522…2df62cb27345af
1 in β†’ 1 out15.6700 XPM108 B
AWdtCUuJ…HscHZriH
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.

7.601 Γ— 10⁹⁴(95-digit number)
76015613657294044438…64208810873422738879
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
7.601 Γ— 10⁹⁴(95-digit number)
76015613657294044438…64208810873422738879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.520 Γ— 10⁹⁡(96-digit number)
15203122731458808887…28417621746845477759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.040 Γ— 10⁹⁡(96-digit number)
30406245462917617775…56835243493690955519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.081 Γ— 10⁹⁡(96-digit number)
60812490925835235551…13670486987381911039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.216 Γ— 10⁹⁢(97-digit number)
12162498185167047110…27340973974763822079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.432 Γ— 10⁹⁢(97-digit number)
24324996370334094220…54681947949527644159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.864 Γ— 10⁹⁢(97-digit number)
48649992740668188440…09363895899055288319
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7

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:57,638,885 XPMΒ·at block #6,799,354 Β· updates every 60s
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