1. #6,817,042TWN11 primes

    Bi-Twin · ⛏️ coinsforall.io

Block #1,372,785

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/17/2015, 11:39:47 AM · Difficulty 10.8083 · 5,444,259 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6a8a4091fb9e261e1305dd058ce9e0f1393ddfd820dfe6c08a31b8b1f424e1f4

Height

#1,372,785

Difficulty

10.808268

Transactions

2

Size

5.62 KB

Version

2

Bits

0aceeaa6

Nonce

1,277,683,753

Timestamp

12/17/2015, 11:39:47 AM

Confirmations

5,444,259

Merkle Root

4c3a64742e3d7db7cc95ab744c17f9aacca2de3bd6fb72940c55757dc26cc8b1
Transactions (2)
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.876 × 10⁹⁵(96-digit number)
18768206663044373451…15888147351595198719
Discovered Prime Numbers
p_k = 2^k × origin − 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 − 1
1.876 × 10⁹⁵(96-digit number)
18768206663044373451…15888147351595198719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.753 × 10⁹⁵(96-digit number)
37536413326088746903…31776294703190397439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.507 × 10⁹⁵(96-digit number)
75072826652177493807…63552589406380794879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.501 × 10⁹⁶(97-digit number)
15014565330435498761…27105178812761589759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.002 × 10⁹⁶(97-digit number)
30029130660870997522…54210357625523179519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.005 × 10⁹⁶(97-digit number)
60058261321741995045…08420715251046359039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.201 × 10⁹⁷(98-digit number)
12011652264348399009…16841430502092718079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.402 × 10⁹⁷(98-digit number)
24023304528696798018…33682861004185436159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.804 × 10⁹⁷(98-digit number)
48046609057393596036…67365722008370872319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
9.609 × 10⁹⁷(98-digit number)
96093218114787192073…34731444016741744639
Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆
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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,780,384 XPM·at block #6,817,043 · updates every 60s
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