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Block #1,103,059

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/13/2015, 7:10:08 PM Β· Difficulty 10.7535 Β· 5,713,516 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
88167fb8b77ce72768307e504060ea1ec68af00910b044b351f0a0c97613c17f
View on Chainz β†—

Height

#1,103,059

Difficulty

10.753523

Transactions

2

Size

425 B

Version

2

Bits

0ac0e6ea

Nonce

657,578,723

Timestamp

6/13/2015, 7:10:08 PM

Confirmations

5,713,516

Mined by

⛏️ P2SHARAQ3UBWgLV8TEggQYVNK9znYhs9BiCS6P

Merkle Root

2ee528ea87090ba1aea4b4943874827f0fb46006b9234a994165f0711d9d2f66
Transactions (2)
Coinbasee48ec7258fe45c…1994e692014da5
1 in β†’ 1 out8.6400 XPM109 B
ARAQ3UBW…s9BiCS6P
72863679c55c04…37caa66ef55504
1 in β†’ 2 out21.3900 XPM226 B
Acb1xA8z…9ActivN8Ac76hjQJ…SCLFXY7N
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.

4.928 Γ— 10⁹⁡(96-digit number)
49283087122099071858…14751259498422122239
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
4.928 Γ— 10⁹⁡(96-digit number)
49283087122099071858…14751259498422122239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.856 Γ— 10⁹⁡(96-digit number)
98566174244198143717…29502518996844244479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.971 Γ— 10⁹⁢(97-digit number)
19713234848839628743…59005037993688488959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.942 Γ— 10⁹⁢(97-digit number)
39426469697679257487…18010075987376977919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.885 Γ— 10⁹⁢(97-digit number)
78852939395358514974…36020151974753955839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.577 Γ— 10⁹⁷(98-digit number)
15770587879071702994…72040303949507911679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.154 Γ— 10⁹⁷(98-digit number)
31541175758143405989…44080607899015823359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.308 Γ— 10⁹⁷(98-digit number)
63082351516286811979…88161215798031646719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.261 Γ— 10⁹⁸(99-digit number)
12616470303257362395…76322431596063293439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.523 Γ— 10⁹⁸(99-digit number)
25232940606514724791…52644863192126586879
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:57,776,733 XPMΒ·at block #6,816,574 Β· updates every 60s
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