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Block #2,123,744

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/19/2017, 11:34:04 AM Β· Difficulty 10.9170 Β· 4,718,683 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9634478e394983d613718cda2a3a4103cdf8e7add2489785fb98c8cfc198f245
View on Chainz β†—

Height

#2,123,744

Difficulty

10.917020

Transactions

1

Size

243 B

Version

2

Bits

0aeac1d9

Nonce

1,307,536,038

Timestamp

5/19/2017, 11:34:04 AM

Confirmations

4,718,683

Mined by

⛏️ P2SHAMMJ7Ku9ctFmjCbBPtKsnh34K5ZYGbYo5z

Merkle Root

66c3fca0364b04221489c1b1b0a123e37508e1d41b847140ed17c6f0ae0f9326
Transactions (1)
Coinbase66c3fca0364b04…17c6f0ae0f9326
1 in β†’ 2 out8.3800 XPM152 B
AMMJ7Ku9…ZYGbYo5zAXbk7f7A…Tx7JECPG
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.

6.448 Γ— 10⁹⁢(97-digit number)
64483610186270910444…82327636693109391359
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
6.448 Γ— 10⁹⁢(97-digit number)
64483610186270910444…82327636693109391359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.289 Γ— 10⁹⁷(98-digit number)
12896722037254182088…64655273386218782719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.579 Γ— 10⁹⁷(98-digit number)
25793444074508364177…29310546772437565439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.158 Γ— 10⁹⁷(98-digit number)
51586888149016728355…58621093544875130879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.031 Γ— 10⁹⁸(99-digit number)
10317377629803345671…17242187089750261759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.063 Γ— 10⁹⁸(99-digit number)
20634755259606691342…34484374179500523519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.126 Γ— 10⁹⁸(99-digit number)
41269510519213382684…68968748359001047039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.253 Γ— 10⁹⁸(99-digit number)
82539021038426765368…37937496718002094079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.650 Γ— 10⁹⁹(100-digit number)
16507804207685353073…75874993436004188159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.301 Γ— 10⁹⁹(100-digit number)
33015608415370706147…51749986872008376319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.603 Γ— 10⁹⁹(100-digit number)
66031216830741412294…03499973744016752639
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:57,983,830 XPMΒ·at block #6,842,426 Β· updates every 60s
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