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Block #1,319,846

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/9/2015, 1:36:51 PM Β· Difficulty 10.8604 Β· 5,486,072 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3b95b56e4460d9012c33814bb746ae65c26c4785115a68999e8b1f661820f18f
View on Chainz β†—

Height

#1,319,846

Difficulty

10.860397

Transactions

2

Size

14.72 KB

Version

2

Bits

0adc42fa

Nonce

141,421,862

Timestamp

11/9/2015, 1:36:51 PM

Confirmations

5,486,072

Mined by

⛏️ P2SHAeNEAVbmF8J4c6H4YCoSaA5z5ioePCc47B

Merkle Root

3cae26017970bdce90a6dc3b19814c46ff5239bd68349d9994b264d578fa91a9
Transactions (2)
Coinbasec367ef5755bc27…c59c95eacbd411
1 in β†’ 1 out8.6100 XPM109 B
AeNEAVbm…oePCc47B
c5a7b797cf53b7…edc43887a6c27f
100 in β†’ 2 out349.6882 XPM14.53 KB
ASaAKK9W…zo41ExGCAQHE5e6H…xDwU3vYU
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.

1.066 Γ— 10⁹⁴(95-digit number)
10667783244494268386…50176060421075814401
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.066 Γ— 10⁹⁴(95-digit number)
10667783244494268386…50176060421075814401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.133 Γ— 10⁹⁴(95-digit number)
21335566488988536772…00352120842151628801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.267 Γ— 10⁹⁴(95-digit number)
42671132977977073545…00704241684303257601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.534 Γ— 10⁹⁴(95-digit number)
85342265955954147090…01408483368606515201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.706 Γ— 10⁹⁡(96-digit number)
17068453191190829418…02816966737213030401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.413 Γ— 10⁹⁡(96-digit number)
34136906382381658836…05633933474426060801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.827 Γ— 10⁹⁡(96-digit number)
68273812764763317672…11267866948852121601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.365 Γ— 10⁹⁢(97-digit number)
13654762552952663534…22535733897704243201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.730 Γ— 10⁹⁢(97-digit number)
27309525105905327069…45071467795408486401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.461 Γ— 10⁹⁢(97-digit number)
54619050211810654138…90142935590816972801
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,691,421 XPMΒ·at block #6,805,917 Β· updates every 60s
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