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Block #913,114

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/28/2015, 10:47:38 AM Β· Difficulty 10.9277 Β· 5,891,093 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d77bfdfdd76e3db80b2817eae544445db0558e5066e051a13ec7d4f1f6338fd3
View on Chainz β†—

Height

#913,114

Difficulty

10.927658

Transactions

2

Size

876 B

Version

2

Bits

0aed7af8

Nonce

1,449,666,972

Timestamp

1/28/2015, 10:47:38 AM

Confirmations

5,891,093

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

309d12a8db194d1ee47fbaed19f47b2a3252fe795bb4e0b64138e785979da925
Transactions (2)
Coinbase7e74a3dd40f1bf…f2f500750b487f
1 in β†’ 1 out8.3800 XPM116 B
ANSXnLY2…Sd25TjkD
8741ebe23c25c1…30e0cf48640adf
4 in β†’ 2 out249.0342 XPM670 B
AUSxVrre…B27XD3yvALnY9ySv…zh7iiDjU
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.

3.773 Γ— 10⁹⁴(95-digit number)
37730325583640074624…19717763991828447761
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
3.773 Γ— 10⁹⁴(95-digit number)
37730325583640074624…19717763991828447761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.546 Γ— 10⁹⁴(95-digit number)
75460651167280149249…39435527983656895521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.509 Γ— 10⁹⁡(96-digit number)
15092130233456029849…78871055967313791041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.018 Γ— 10⁹⁡(96-digit number)
30184260466912059699…57742111934627582081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.036 Γ— 10⁹⁡(96-digit number)
60368520933824119399…15484223869255164161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.207 Γ— 10⁹⁢(97-digit number)
12073704186764823879…30968447738510328321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.414 Γ— 10⁹⁢(97-digit number)
24147408373529647759…61936895477020656641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.829 Γ— 10⁹⁢(97-digit number)
48294816747059295519…23873790954041313281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.658 Γ— 10⁹⁢(97-digit number)
96589633494118591039…47747581908082626561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.931 Γ— 10⁹⁷(98-digit number)
19317926698823718207…95495163816165253121
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:57,677,704 XPMΒ·at block #6,804,206 Β· updates every 60s
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