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Block #1,589,193

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/17/2016, 11:09:08 PM Β· Difficulty 10.6519 Β· 5,256,194 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8466b0b8a22a8224ffa85a5ff4e02801c1db1246c1e4f7d2709e45949b13a279
View on Chainz β†—

Height

#1,589,193

Difficulty

10.651950

Transactions

1

Size

200 B

Version

2

Bits

0aa6e62f

Nonce

102,021,847

Timestamp

5/17/2016, 11:09:08 PM

Confirmations

5,256,194

Mined by

⛏️ P2SHAc1aryjmJ6rkGtcZxduKZxMrzz9JacVJwJ

Merkle Root

ad70e54c400f07b257089905d05447629b8a377f466ef6f41a79cc713d86b68e
Transactions (1)
Coinbasead70e54c400f07…79cc713d86b68e
1 in β†’ 1 out8.8000 XPM110 B
Ac1aryjm…9JacVJwJ
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.

9.914 Γ— 10⁹⁴(95-digit number)
99141278643171434558…74079277154591924479
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
9.914 Γ— 10⁹⁴(95-digit number)
99141278643171434558…74079277154591924479
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)
19828255728634286911…48158554309183848959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.965 Γ— 10⁹⁡(96-digit number)
39656511457268573823…96317108618367697919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.931 Γ— 10⁹⁡(96-digit number)
79313022914537147646…92634217236735395839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.586 Γ— 10⁹⁢(97-digit number)
15862604582907429529…85268434473470791679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.172 Γ— 10⁹⁢(97-digit number)
31725209165814859058…70536868946941583359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.345 Γ— 10⁹⁢(97-digit number)
63450418331629718117…41073737893883166719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.269 Γ— 10⁹⁷(98-digit number)
12690083666325943623…82147475787766333439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.538 Γ— 10⁹⁷(98-digit number)
25380167332651887246…64294951575532666879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.076 Γ— 10⁹⁷(98-digit number)
50760334665303774493…28589903151065333759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.015 Γ— 10⁹⁸(99-digit number)
10152066933060754898…57179806302130667519
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:58,007,541 XPMΒ·at block #6,845,386 Β· updates every 60s
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