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Block #1,398,623

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/4/2016, 11:11:39 AM Β· Difficulty 10.8071 Β· 5,413,504 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fc8bd98d4bb0a7bbe7d535abd4001a89274589fdbdaa7fb24006f244ae83144e
View on Chainz β†—

Height

#1,398,623

Difficulty

10.807149

Transactions

2

Size

12.85 KB

Version

2

Bits

0acea152

Nonce

1,103,299,243

Timestamp

1/4/2016, 11:11:39 AM

Confirmations

5,413,504

Mined by

⛏️ P2SHAPjAjK8FKAqCzQ1mNUhJqEtbS9FVgW2Cwd

Merkle Root

415f004f430f126dc0a4f341aaf38f7b6f889dd1c5eab8cdedbe53da1fb1847c
Transactions (2)
Coinbase75251e628b54aa…2bc487830133a2
1 in β†’ 1 out8.6800 XPM110 B
APjAjK8F…FVgW2Cwd
603405409e3f47…03449877992923
87 in β†’ 2 out634.7599 XPM12.65 KB
AHNccZy4…RwZSfQd3AavP4aiu…SnVpekp4
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.

8.098 Γ— 10⁹⁴(95-digit number)
80985340375845757435…74039407631791275999
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
8.098 Γ— 10⁹⁴(95-digit number)
80985340375845757435…74039407631791275999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.619 Γ— 10⁹⁡(96-digit number)
16197068075169151487…48078815263582551999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.239 Γ— 10⁹⁡(96-digit number)
32394136150338302974…96157630527165103999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.478 Γ— 10⁹⁡(96-digit number)
64788272300676605948…92315261054330207999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.295 Γ— 10⁹⁢(97-digit number)
12957654460135321189…84630522108660415999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.591 Γ— 10⁹⁢(97-digit number)
25915308920270642379…69261044217320831999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.183 Γ— 10⁹⁢(97-digit number)
51830617840541284758…38522088434641663999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.036 Γ— 10⁹⁷(98-digit number)
10366123568108256951…77044176869283327999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.073 Γ— 10⁹⁷(98-digit number)
20732247136216513903…54088353738566655999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.146 Γ— 10⁹⁷(98-digit number)
41464494272433027806…08176707477133311999
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:57,741,028 XPMΒ·at block #6,812,126 Β· updates every 60s
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