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Block #1,371,647

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/16/2015, 3:33:00 PM Β· Difficulty 10.8108 Β· 5,468,563 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
efb42b831006e81e971d846220d4d34b4e13dbb9809ca95bbbb1f429837b040d
View on Chainz β†—

Height

#1,371,647

Difficulty

10.810759

Transactions

1

Size

200 B

Version

2

Bits

0acf8de5

Nonce

225,552,433

Timestamp

12/16/2015, 3:33:00 PM

Confirmations

5,468,563

Mined by

⛏️ P2SHAe3B6xFXoHm8yELLZwTaDSFy25FPittGJ4

Merkle Root

92e68a2c4b7a3a426accf19e739dff9c3a6f16dde074caf1e1fa054ef83b5ad2
Transactions (1)
Coinbase92e68a2c4b7a3a…fa054ef83b5ad2
1 in β†’ 1 out8.5400 XPM110 B
Ae3B6xFX…FPittGJ4
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.

9.001 Γ— 10⁹⁴(95-digit number)
90010115014959894317…66848633171666603521
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
9.001 Γ— 10⁹⁴(95-digit number)
90010115014959894317…66848633171666603521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.800 Γ— 10⁹⁡(96-digit number)
18002023002991978863…33697266343333207041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.600 Γ— 10⁹⁡(96-digit number)
36004046005983957726…67394532686666414081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.200 Γ— 10⁹⁡(96-digit number)
72008092011967915453…34789065373332828161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.440 Γ— 10⁹⁢(97-digit number)
14401618402393583090…69578130746665656321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.880 Γ— 10⁹⁢(97-digit number)
28803236804787166181…39156261493331312641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.760 Γ— 10⁹⁢(97-digit number)
57606473609574332362…78312522986662625281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.152 Γ— 10⁹⁷(98-digit number)
11521294721914866472…56625045973325250561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.304 Γ— 10⁹⁷(98-digit number)
23042589443829732945…13250091946650501121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.608 Γ— 10⁹⁷(98-digit number)
46085178887659465890…26500183893301002241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.217 Γ— 10⁹⁷(98-digit number)
92170357775318931780…53000367786602004481
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 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
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,965,998 XPMΒ·at block #6,840,209 Β· updates every 60s
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