Block #956,456

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/1/2015, 1:28:14 AM · Difficulty 10.8907 · 5,853,166 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
984bb7c3660fea4def87b9eba365ebf267fa348e4f43514139113e218427eb2b

Height

#956,456

Difficulty

10.890706

Transactions

2

Size

2.05 KB

Version

2

Bits

0ae40553

Nonce

17,984,857

Timestamp

3/1/2015, 1:28:14 AM

Confirmations

5,853,166

Merkle Root

cbc1f4134efd74f1c5b2e348279639302fc9adc96222d2070a20a502b995cc1c
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.

3.523 × 10⁹⁵(96-digit number)
35233935485385247428…38396904349440280081
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
3.523 × 10⁹⁵(96-digit number)
35233935485385247428…38396904349440280081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.046 × 10⁹⁵(96-digit number)
70467870970770494857…76793808698880560161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.409 × 10⁹⁶(97-digit number)
14093574194154098971…53587617397761120321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.818 × 10⁹⁶(97-digit number)
28187148388308197943…07175234795522240641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.637 × 10⁹⁶(97-digit number)
56374296776616395886…14350469591044481281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.127 × 10⁹⁷(98-digit number)
11274859355323279177…28700939182088962561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.254 × 10⁹⁷(98-digit number)
22549718710646558354…57401878364177925121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.509 × 10⁹⁷(98-digit number)
45099437421293116708…14803756728355850241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.019 × 10⁹⁷(98-digit number)
90198874842586233417…29607513456711700481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.803 × 10⁹⁸(99-digit number)
18039774968517246683…59215026913423400961
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,721,054 XPM·at block #6,809,621 · updates every 60s
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