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Block #918,476

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/1/2015, 10:18:47 AM Β· Difficulty 10.9224 Β· 5,877,493 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e9b8ab56b75ec137a2326ae7446b201e50f9a60072f19eeb3f6b65ed32b1b9c1
View on Chainz β†—

Height

#918,476

Difficulty

10.922374

Transactions

2

Size

4.47 KB

Version

2

Bits

0aec20b5

Nonce

126,628,052

Timestamp

2/1/2015, 10:18:47 AM

Confirmations

5,877,493

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

538cb84d90a10efa037186fbfe374c40410c7a1697a5ea6049203a9133351ab7
Transactions (2)
Coinbase12875409b91fb0…381b7a8b3a0dc6
1 in β†’ 1 out8.4200 XPM116 B
ANSXnLY2…Sd25TjkD
21fa455e603cd5…f57d7d5cf1ff44
29 in β†’ 2 out1342.3866 XPM4.27 KB
ATv9L3qR…63UMNKM2AUo2igs3…6HSSeLKF
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.

9.805 Γ— 10⁹⁡(96-digit number)
98053949407313527473…49918283357057181439
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
9.805 Γ— 10⁹⁡(96-digit number)
98053949407313527473…49918283357057181439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.961 Γ— 10⁹⁢(97-digit number)
19610789881462705494…99836566714114362879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.922 Γ— 10⁹⁢(97-digit number)
39221579762925410989…99673133428228725759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.844 Γ— 10⁹⁢(97-digit number)
78443159525850821978…99346266856457451519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.568 Γ— 10⁹⁷(98-digit number)
15688631905170164395…98692533712914903039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.137 Γ— 10⁹⁷(98-digit number)
31377263810340328791…97385067425829806079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.275 Γ— 10⁹⁷(98-digit number)
62754527620680657583…94770134851659612159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.255 Γ— 10⁹⁸(99-digit number)
12550905524136131516…89540269703319224319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.510 Γ— 10⁹⁸(99-digit number)
25101811048272263033…79080539406638448639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.020 Γ— 10⁹⁸(99-digit number)
50203622096544526066…58161078813276897279
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,611,844 XPMΒ·at block #6,795,968 Β· updates every 60s
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