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Home/Chain Registry/Block #1,408,660

Block #1,408,660

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/11/2016, 11:27:36 AM Β· Difficulty 10.8051 Β· 5,433,743 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2d6949328fcc558f95365a3019f6150da15170f6320d32863fa014d5dd2703fe
View on Chainz β†—

Difficulty

10.805110

Transactions

1

Size

200 B

Version

2

Bits

0ace1bb5

Nonce

598,236,521

Timestamp

1/11/2016, 11:27:36 AM

Confirmations

5,433,743

Merkle Root

d861848bf065e1a60f5ee5b9fe8f4cb16b58c6bbb30e8d9257142cbbb151e02d
Transactions (1)
Coinbased861848bf065e1…142cbbb151e02d
1 in β†’ 1 out8.5500 XPM109 B
AXnWiXRP…3L5yKYfu
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.

6.752 Γ— 10⁹⁷(98-digit number)
67523765482284472078…97958962760742338560
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
6.752 Γ— 10⁹⁷(98-digit number)
67523765482284472078…97958962760742338559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.752 Γ— 10⁹⁷(98-digit number)
67523765482284472078…97958962760742338561
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
1.350 Γ— 10⁹⁸(99-digit number)
13504753096456894415…95917925521484677119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.350 Γ— 10⁹⁸(99-digit number)
13504753096456894415…95917925521484677121
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
2.700 Γ— 10⁹⁸(99-digit number)
27009506192913788831…91835851042969354239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.700 Γ— 10⁹⁸(99-digit number)
27009506192913788831…91835851042969354241
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
5.401 Γ— 10⁹⁸(99-digit number)
54019012385827577662…83671702085938708479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.401 Γ— 10⁹⁸(99-digit number)
54019012385827577662…83671702085938708481
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
1.080 Γ— 10⁹⁹(100-digit number)
10803802477165515532…67343404171877416959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.080 Γ— 10⁹⁹(100-digit number)
10803802477165515532…67343404171877416961
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
2.160 Γ— 10⁹⁹(100-digit number)
21607604954331031064…34686808343754833919
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 1408660

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 2d6949328fcc558f95365a3019f6150da15170f6320d32863fa014d5dd2703fe

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 #1,408,660 on Chainz β†—
Circulating Supply:57,983,635 XPMΒ·at block #6,842,402 Β· updates every 60s
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