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Block #1,368,319

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/13/2015, 8:03:38 PM Β· Difficulty 10.8359 Β· 5,465,060 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
83772470cd991f2aee8cc223087f69723c0c05b4be3a6c1faf6bf9186a3a8d95
View on Chainz β†—

Height

#1,368,319

Difficulty

10.835931

Transactions

1

Size

200 B

Version

2

Bits

0ad5ff8c

Nonce

1,670,858,521

Timestamp

12/13/2015, 8:03:38 PM

Confirmations

5,465,060

Mined by

⛏️ P2SHAWfbddtWngqv8FgQaWmdRHQcFf9e9P8DYF

Merkle Root

4bdef7c19ef4a968904068778f6ac35f2c0cfba47ef519c388462b7bcd63a10d
Transactions (1)
Coinbase4bdef7c19ef4a9…462b7bcd63a10d
1 in β†’ 1 out8.5000 XPM110 B
AWfbddtW…9e9P8DYF
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.

1.221 Γ— 10⁹⁴(95-digit number)
12216956453288359993…73485767611768062719
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
1.221 Γ— 10⁹⁴(95-digit number)
12216956453288359993…73485767611768062719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.443 Γ— 10⁹⁴(95-digit number)
24433912906576719987…46971535223536125439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.886 Γ— 10⁹⁴(95-digit number)
48867825813153439974…93943070447072250879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.773 Γ— 10⁹⁴(95-digit number)
97735651626306879949…87886140894144501759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.954 Γ— 10⁹⁡(96-digit number)
19547130325261375989…75772281788289003519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.909 Γ— 10⁹⁡(96-digit number)
39094260650522751979…51544563576578007039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.818 Γ— 10⁹⁡(96-digit number)
78188521301045503959…03089127153156014079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.563 Γ— 10⁹⁢(97-digit number)
15637704260209100791…06178254306312028159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.127 Γ— 10⁹⁢(97-digit number)
31275408520418201583…12356508612624056319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.255 Γ— 10⁹⁢(97-digit number)
62550817040836403167…24713017225248112639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.251 Γ— 10⁹⁷(98-digit number)
12510163408167280633…49426034450496225279
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:57,911,229 XPMΒ·at block #6,833,378 Β· updates every 60s
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