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Block #2,154,334

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/10/2017, 6:29:02 AM Β· Difficulty 10.9039 Β· 4,689,029 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
436fbc71e26151a51598a886ead4fda071f26fd9296e943e6d0cdc26f8883d04
View on Chainz β†—

Height

#2,154,334

Difficulty

10.903941

Transactions

2

Size

867 B

Version

2

Bits

0ae768b2

Nonce

1,352,632,140

Timestamp

6/10/2017, 6:29:02 AM

Confirmations

4,689,029

Mined by

⛏️ P2SHAZAdwsaXRoayxk544iKVoWBEf64YWcJoia

Merkle Root

9e38f541053f3f2c15530d8b46094a528aa57994d6dbad528df223965e307c41
Transactions (2)
Coinbasecc50ac14c0e71b…e95cf5bcc91b95
1 in β†’ 1 out8.4100 XPM110 B
AZAdwsaX…4YWcJoia
257e8db5381e20…885ed1a4503a04
4 in β†’ 2 out1881.0113 XPM668 B
APUX7Qs9…R7xGLxDAARsuhVkc…w3M6D8DV
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.

3.032 Γ— 10⁹³(94-digit number)
30328635058006540772…63799837612344379201
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
3.032 Γ— 10⁹³(94-digit number)
30328635058006540772…63799837612344379201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.065 Γ— 10⁹³(94-digit number)
60657270116013081544…27599675224688758401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.213 Γ— 10⁹⁴(95-digit number)
12131454023202616308…55199350449377516801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.426 Γ— 10⁹⁴(95-digit number)
24262908046405232617…10398700898755033601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.852 Γ— 10⁹⁴(95-digit number)
48525816092810465235…20797401797510067201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.705 Γ— 10⁹⁴(95-digit number)
97051632185620930471…41594803595020134401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.941 Γ— 10⁹⁡(96-digit number)
19410326437124186094…83189607190040268801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.882 Γ— 10⁹⁡(96-digit number)
38820652874248372188…66379214380080537601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.764 Γ— 10⁹⁡(96-digit number)
77641305748496744377…32758428760161075201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.552 Γ— 10⁹⁢(97-digit number)
15528261149699348875…65516857520322150401
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:57,991,266 XPMΒ·at block #6,843,362 Β· updates every 60s
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