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Block #2,647,748

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/4/2018, 2:35:04 AM Β· Difficulty 11.7622 Β· 4,195,553 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
97a0e9e8e1ef38597c73a0ddaf24c49fd323fa127dc9f1710647ca45703cc1d0
View on Chainz β†—

Height

#2,647,748

Difficulty

11.762159

Transactions

1

Size

199 B

Version

2

Bits

0bc31cd2

Nonce

665,520,941

Timestamp

5/4/2018, 2:35:04 AM

Confirmations

4,195,553

Mined by

⛏️ P2SHAZXxLZMWcWFq6AMYdzG6CdeDQnLmDY3yCy

Merkle Root

5162f4b9f1b868fce2a5e0ed8bd08eb75a4e28e38aa99ed8b11735451f515d70
Transactions (1)
Coinbase5162f4b9f1b868…1735451f515d70
1 in β†’ 1 out7.2200 XPM109 B
AZXxLZMW…LmDY3yCy
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.

1.247 Γ— 10⁹⁴(95-digit number)
12479048330755444090…78501227721219079759
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
1.247 Γ— 10⁹⁴(95-digit number)
12479048330755444090…78501227721219079759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.495 Γ— 10⁹⁴(95-digit number)
24958096661510888180…57002455442438159519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.991 Γ— 10⁹⁴(95-digit number)
49916193323021776360…14004910884876319039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.983 Γ— 10⁹⁴(95-digit number)
99832386646043552721…28009821769752638079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.996 Γ— 10⁹⁡(96-digit number)
19966477329208710544…56019643539505276159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.993 Γ— 10⁹⁡(96-digit number)
39932954658417421088…12039287079010552319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.986 Γ— 10⁹⁡(96-digit number)
79865909316834842177…24078574158021104639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.597 Γ— 10⁹⁢(97-digit number)
15973181863366968435…48157148316042209279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.194 Γ— 10⁹⁢(97-digit number)
31946363726733936870…96314296632084418559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.389 Γ— 10⁹⁢(97-digit number)
63892727453467873741…92628593264168837119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.277 Γ— 10⁹⁷(98-digit number)
12778545490693574748…85257186528337674239
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,990,773 XPMΒ·at block #6,843,300 Β· updates every 60s
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