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Block #2,148,152

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/6/2017, 6:53:58 AM Β· Difficulty 10.8948 Β· 4,692,414 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4ccd4e65d68a57a9c64ee88c7ac5a868292de24756dd81bdf7bb9dca9d1dec17
View on Chainz β†—

Height

#2,148,152

Difficulty

10.894824

Transactions

2

Size

425 B

Version

2

Bits

0ae51332

Nonce

89,237,439

Timestamp

6/6/2017, 6:53:58 AM

Confirmations

4,692,414

Mined by

⛏️ P2SHAKeNGaHR2q1u4ShQbfvDhuws8zRdTmF9CU

Merkle Root

bdfbc34f86689da83cf4358d7eb86b433be3c71f3db26fe2842e3e2c3250fea3
Transactions (2)
Coinbase399bc4bb9f7899…4de781c153379f
1 in β†’ 1 out8.4200 XPM109 B
AKeNGaHR…RdTmF9CU
c779baca833bc3…866af78fc50be2
1 in β†’ 2 out203.4546 XPM226 B
AVEwBD6K…ua7smMQLAUfiNpNR…r4iERJXe
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.

9.531 Γ— 10⁹⁴(95-digit number)
95317907019353561279…51823695439184097281
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
9.531 Γ— 10⁹⁴(95-digit number)
95317907019353561279…51823695439184097281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.906 Γ— 10⁹⁡(96-digit number)
19063581403870712255…03647390878368194561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.812 Γ— 10⁹⁡(96-digit number)
38127162807741424511…07294781756736389121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.625 Γ— 10⁹⁡(96-digit number)
76254325615482849023…14589563513472778241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.525 Γ— 10⁹⁢(97-digit number)
15250865123096569804…29179127026945556481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.050 Γ— 10⁹⁢(97-digit number)
30501730246193139609…58358254053891112961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.100 Γ— 10⁹⁢(97-digit number)
61003460492386279219…16716508107782225921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.220 Γ— 10⁹⁷(98-digit number)
12200692098477255843…33433016215564451841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.440 Γ— 10⁹⁷(98-digit number)
24401384196954511687…66866032431128903681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.880 Γ— 10⁹⁷(98-digit number)
48802768393909023375…33732064862257807361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.760 Γ— 10⁹⁷(98-digit number)
97605536787818046750…67464129724515614721
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:57,968,863 XPMΒ·at block #6,840,565 Β· updates every 60s
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