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Block #901,455

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/19/2015, 1:53:43 PM Β· Difficulty 10.9417 Β· 5,896,973 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
49738b7f8bd63012564300d2cde1d3d50745610fca24f9f2a4c2e76a3c5b4d52
View on Chainz β†—

Height

#901,455

Difficulty

10.941692

Transactions

1

Size

242 B

Version

2

Bits

0af112b4

Nonce

261,608,453

Timestamp

1/19/2015, 1:53:43 PM

Confirmations

5,896,973

Merkle Root

c3ff6b8775e888130a1d11c2b4e16bbb8d9596d2f34441df52ab588fcb152650
Transactions (1)
Coinbasec3ff6b8775e888…ab588fcb152650
1 in β†’ 2 out8.3400 XPM152 B
AWEVBqpf…LjqpnMdSALPu3s2c…EJXLjVFh
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.

4.754 Γ— 10⁹⁡(96-digit number)
47543572691045961379…48712048155933489200
Discovered Prime Numbers
p_k = 2^k Γ— 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
4.754 Γ— 10⁹⁡(96-digit number)
47543572691045961379…48712048155933489201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.508 Γ— 10⁹⁡(96-digit number)
95087145382091922758…97424096311866978401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.901 Γ— 10⁹⁢(97-digit number)
19017429076418384551…94848192623733956801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.803 Γ— 10⁹⁢(97-digit number)
38034858152836769103…89696385247467913601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.606 Γ— 10⁹⁢(97-digit number)
76069716305673538207…79392770494935827201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.521 Γ— 10⁹⁷(98-digit number)
15213943261134707641…58785540989871654401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.042 Γ— 10⁹⁷(98-digit number)
30427886522269415282…17571081979743308801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.085 Γ— 10⁹⁷(98-digit number)
60855773044538830565…35142163959486617601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.217 Γ— 10⁹⁸(99-digit number)
12171154608907766113…70284327918973235201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.434 Γ— 10⁹⁸(99-digit number)
24342309217815532226…40568655837946470401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.868 Γ— 10⁹⁸(99-digit number)
48684618435631064452…81137311675892940801
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 Second 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.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 901455

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 49738b7f8bd63012564300d2cde1d3d50745610fca24f9f2a4c2e76a3c5b4d52

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #901,455 on Chainz β†—
Circulating Supply:57,631,436 XPMΒ·at block #6,798,427 Β· updates every 60s
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