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Block #1,273,470

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/9/2015, 3:31:43 AM Β· Difficulty 10.8237 Β· 5,553,453 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e32779dcaac112f03345d0e5039db9da4cb642df14096ce17b9fddcf55e9f412
View on Chainz β†—

Height

#1,273,470

Difficulty

10.823659

Transactions

2

Size

459 B

Version

2

Bits

0ad2db54

Nonce

933,481,151

Timestamp

10/9/2015, 3:31:43 AM

Confirmations

5,553,453

Mined by

⛏️ P2SHAFp9MujH8gpBNwTvNNdkJgTasax9n93DAq

Merkle Root

ab2a3d92a674b789f31fa794def9fabc564be38f65b3411a4cf025160bb93e84
Transactions (2)
Coinbasea6fc5c7d3cdb35…b1c7b5a1e1cf99
1 in β†’ 1 out8.5300 XPM109 B
AFp9MujH…x9n93DAq
efab4973fcca82…b5a7b08872d7b4
1 in β†’ 3 out17.5334 XPM260 B
AGMWpDx8…Ve94zjALAKsebF9o…26T4a6vnAR6qgsuL…x1tjMz93
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.

1.073 Γ— 10⁹⁴(95-digit number)
10734542768441139060…32381886014668126099
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
1.073 Γ— 10⁹⁴(95-digit number)
10734542768441139060…32381886014668126099
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.146 Γ— 10⁹⁴(95-digit number)
21469085536882278120…64763772029336252199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.293 Γ— 10⁹⁴(95-digit number)
42938171073764556241…29527544058672504399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.587 Γ— 10⁹⁴(95-digit number)
85876342147529112482…59055088117345008799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.717 Γ— 10⁹⁡(96-digit number)
17175268429505822496…18110176234690017599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.435 Γ— 10⁹⁡(96-digit number)
34350536859011644992…36220352469380035199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.870 Γ— 10⁹⁡(96-digit number)
68701073718023289985…72440704938760070399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.374 Γ— 10⁹⁢(97-digit number)
13740214743604657997…44881409877520140799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.748 Γ— 10⁹⁢(97-digit number)
27480429487209315994…89762819755040281599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.496 Γ— 10⁹⁢(97-digit number)
54960858974418631988…79525639510080563199
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:57,859,555 XPMΒ·at block #6,826,922 Β· updates every 60s
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