XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #612,886

Block #612,886

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/2/2014, 8:56:20 PM Β· Difficulty 10.9291 Β· 6,181,765 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
e357c19cd6ecff049ecacb6cb0fb2f54fea2a5c3bb99fe79c0d3bb6d37e79d16
View on Chainz β†—

Height

#612,886

Difficulty

10.929063

Transactions

1

Size

201 B

Version

2

Bits

0aedd70e

Nonce

637,495

Timestamp

7/2/2014, 8:56:20 PM

Confirmations

6,181,765

Merkle Root

02bc45ad802162efedddf1410de676cbeee10bb653b2721a3b16b6cf06ba2c25
Transactions (1)
Coinbase02bc45ad802162…16b6cf06ba2c25
1 in β†’ 1 out8.3600 XPM110 B
AeKNrjNj…1NEq95Ta
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.

5.798 Γ— 10⁹⁢(97-digit number)
57985143458785438250…17464606614621606150
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
5.798 Γ— 10⁹⁢(97-digit number)
57985143458785438250…17464606614621606149
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.798 Γ— 10⁹⁢(97-digit number)
57985143458785438250…17464606614621606151
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.159 Γ— 10⁹⁷(98-digit number)
11597028691757087650…34929213229243212299
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.159 Γ— 10⁹⁷(98-digit number)
11597028691757087650…34929213229243212301
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.319 Γ— 10⁹⁷(98-digit number)
23194057383514175300…69858426458486424599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.319 Γ— 10⁹⁷(98-digit number)
23194057383514175300…69858426458486424601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
4.638 Γ— 10⁹⁷(98-digit number)
46388114767028350600…39716852916972849199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.638 Γ— 10⁹⁷(98-digit number)
46388114767028350600…39716852916972849201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
9.277 Γ— 10⁹⁷(98-digit number)
92776229534056701200…79433705833945698399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.277 Γ— 10⁹⁷(98-digit number)
92776229534056701200…79433705833945698401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.855 Γ— 10⁹⁸(99-digit number)
18555245906811340240…58867411667891396799
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 Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 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 612886

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 e357c19cd6ecff049ecacb6cb0fb2f54fea2a5c3bb99fe79c0d3bb6d37e79d16

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 #612,886 on Chainz β†—
Circulating Supply:57,601,257 XPMΒ·at block #6,794,650 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK