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Block #1,303,508

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/29/2015, 7:40:05 AM Β· Difficulty 10.8559 Β· 5,504,558 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0871cad18df6115d8b15a54e1722940825802a710b3ae49de38fc66b8eca91be
View on Chainz β†—

Height

#1,303,508

Difficulty

10.855904

Transactions

2

Size

1.72 KB

Version

2

Bits

0adb1c81

Nonce

361,045,210

Timestamp

10/29/2015, 7:40:05 AM

Confirmations

5,504,558

Mined by

⛏️ P2SHAM2W5gWc7KtumXmQALDjeh9YTbx461B82F

Merkle Root

5a8e1f094b25af6968652f41ae15b608cde7d20c23d2e70abbaf5a4b79740318
Transactions (2)
Coinbasedeb266f03eebcc…aa08ef3ce56fb9
1 in β†’ 1 out8.4900 XPM110 B
AM2W5gWc…x461B82F
d9b5e5f7a92547…369f38e82e347a
10 in β†’ 2 out50000.0100 XPM1.52 KB
AYKArr5V…V9VqiqCZARA89k5i…YYyMVFQK
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.

1.373 Γ— 10⁹⁴(95-digit number)
13731570127921039537…58123480616397029439
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
1.373 Γ— 10⁹⁴(95-digit number)
13731570127921039537…58123480616397029439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.746 Γ— 10⁹⁴(95-digit number)
27463140255842079075…16246961232794058879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.492 Γ— 10⁹⁴(95-digit number)
54926280511684158151…32493922465588117759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.098 Γ— 10⁹⁡(96-digit number)
10985256102336831630…64987844931176235519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.197 Γ— 10⁹⁡(96-digit number)
21970512204673663260…29975689862352471039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.394 Γ— 10⁹⁡(96-digit number)
43941024409347326521…59951379724704942079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.788 Γ— 10⁹⁡(96-digit number)
87882048818694653043…19902759449409884159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.757 Γ— 10⁹⁢(97-digit number)
17576409763738930608…39805518898819768319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.515 Γ— 10⁹⁢(97-digit number)
35152819527477861217…79611037797639536639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.030 Γ— 10⁹⁢(97-digit number)
70305639054955722434…59222075595279073279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.406 Γ— 10⁹⁷(98-digit number)
14061127810991144486…18444151190558146559
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:57,708,573 XPMΒ·at block #6,808,065 Β· updates every 60s
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