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Block #2,103,600

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/6/2017, 9:13:50 PM Β· Difficulty 10.8757 Β· 4,728,459 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
91e39b051e1578d89f1d2bfe4b66ceb87bd6c0dac3701371b59cbd27c6fefe34
View on Chainz β†—

Height

#2,103,600

Difficulty

10.875694

Transactions

2

Size

2.00 KB

Version

2

Bits

0ae02d82

Nonce

1,097,343,263

Timestamp

5/6/2017, 9:13:50 PM

Confirmations

4,728,459

Mined by

⛏️ P2SHAc8g7qraqqAMk8pmD2zizuBMmWD4o8HB6m

Merkle Root

7812d29426dd438457e7f2f0dfef17b4fee7558225838dbadd25b4196c640c0a
Transactions (2)
Coinbasef6272cea0c7246…857a283d31689b
1 in β†’ 1 out8.4600 XPM109 B
Ac8g7qra…D4o8HB6m
b6da4f96b77c56…372df70bcd2747
14 in β†’ 2 out83.5066 XPM1.80 KB
ANca5fao…7raYLQ7oAVEfhJ1b…G1HPVjLz
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.

1.479 Γ— 10⁹⁷(98-digit number)
14790715388616600885…33227274462598737919
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
1.479 Γ— 10⁹⁷(98-digit number)
14790715388616600885…33227274462598737919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.958 Γ— 10⁹⁷(98-digit number)
29581430777233201771…66454548925197475839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.916 Γ— 10⁹⁷(98-digit number)
59162861554466403542…32909097850394951679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.183 Γ— 10⁹⁸(99-digit number)
11832572310893280708…65818195700789903359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.366 Γ— 10⁹⁸(99-digit number)
23665144621786561417…31636391401579806719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.733 Γ— 10⁹⁸(99-digit number)
47330289243573122834…63272782803159613439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.466 Γ— 10⁹⁸(99-digit number)
94660578487146245668…26545565606319226879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.893 Γ— 10⁹⁹(100-digit number)
18932115697429249133…53091131212638453759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.786 Γ— 10⁹⁹(100-digit number)
37864231394858498267…06182262425276907519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.572 Γ— 10⁹⁹(100-digit number)
75728462789716996534…12364524850553815039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.514 Γ— 10¹⁰⁰(101-digit number)
15145692557943399306…24729049701107630079
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,900,604 XPMΒ·at block #6,832,058 Β· updates every 60s
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