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Block #223,115

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/22/2013, 6:05:23 PM Β· Difficulty 9.9389 Β· 6,573,631 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
da8aea060bbea7c967fbf757e5486410ea35fce0b559518aa77aa885133aeccb
View on Chainz β†—

Height

#223,115

Difficulty

9.938859

Transactions

1

Size

196 B

Version

2

Bits

09f05916

Nonce

54,580

Timestamp

10/22/2013, 6:05:23 PM

Confirmations

6,573,631

Mined by

⛏️ P2SHAXHqpR716k7HAKyiRQyC63yPtEEXddpMfV

Merkle Root

bf112a70280890d08db57088c09873e475839ad9faed72eff62093a21fe71008
Transactions (1)
Coinbasebf112a70280890…2093a21fe71008
1 in β†’ 1 out10.1100 XPM109 B
AXHqpR71…EXddpMfV
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.

6.247 Γ— 10⁸⁷(88-digit number)
62470748919488174831…30729707223173920479
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
6.247 Γ— 10⁸⁷(88-digit number)
62470748919488174831…30729707223173920479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.249 Γ— 10⁸⁸(89-digit number)
12494149783897634966…61459414446347840959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.498 Γ— 10⁸⁸(89-digit number)
24988299567795269932…22918828892695681919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.997 Γ— 10⁸⁸(89-digit number)
49976599135590539865…45837657785391363839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.995 Γ— 10⁸⁸(89-digit number)
99953198271181079730…91675315570782727679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.999 Γ— 10⁸⁹(90-digit number)
19990639654236215946…83350631141565455359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.998 Γ— 10⁸⁹(90-digit number)
39981279308472431892…66701262283130910719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.996 Γ— 10⁸⁹(90-digit number)
79962558616944863784…33402524566261821439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.599 Γ— 10⁹⁰(91-digit number)
15992511723388972756…66805049132523642879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.198 Γ— 10⁹⁰(91-digit number)
31985023446777945513…33610098265047285759
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,617,977 XPMΒ·at block #6,796,745 Β· updates every 60s
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