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Block #2,117,577

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/15/2017, 2:57:41 PM Β· Difficulty 10.9061 Β· 4,723,957 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2c7646a060711d0f5c21d57ef44c1c0b1a4eee7a0c69e5e77b260b99cfb9a068
View on Chainz β†—

Height

#2,117,577

Difficulty

10.906089

Transactions

1

Size

243 B

Version

2

Bits

0ae7f579

Nonce

2,884,988,037

Timestamp

5/15/2017, 2:57:41 PM

Confirmations

4,723,957

Mined by

⛏️ P2SHAMMJ7Ku9ctFmjCbBPtKsnh34K5ZYGbYo5z

Merkle Root

9aae53ad74f1f83d23b6edb3360f64e0d1e1e5bbddb09e861db8fc3dbb9b8a9d
Transactions (1)
Coinbase9aae53ad74f1f8…b8fc3dbb9b8a9d
1 in β†’ 2 out8.3900 XPM152 B
AMMJ7Ku9…ZYGbYo5zAXbk7f7A…Tx7JECPG
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.

1.531 Γ— 10⁹⁷(98-digit number)
15318356166579337080…87643891369027264001
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
1.531 Γ— 10⁹⁷(98-digit number)
15318356166579337080…87643891369027264001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.063 Γ— 10⁹⁷(98-digit number)
30636712333158674160…75287782738054528001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.127 Γ— 10⁹⁷(98-digit number)
61273424666317348321…50575565476109056001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.225 Γ— 10⁹⁸(99-digit number)
12254684933263469664…01151130952218112001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.450 Γ— 10⁹⁸(99-digit number)
24509369866526939328…02302261904436224001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.901 Γ— 10⁹⁸(99-digit number)
49018739733053878656…04604523808872448001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.803 Γ— 10⁹⁸(99-digit number)
98037479466107757313…09209047617744896001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.960 Γ— 10⁹⁹(100-digit number)
19607495893221551462…18418095235489792001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.921 Γ— 10⁹⁹(100-digit number)
39214991786443102925…36836190470979584001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.842 Γ— 10⁹⁹(100-digit number)
78429983572886205850…73672380941959168001
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:57,976,655 XPMΒ·at block #6,841,533 Β· updates every 60s
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