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Block #252,141

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/9/2013, 9:59:39 AM Β· Difficulty 9.9708 Β· 6,544,168 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1002933c774d76590fc820ffd51b3dae13f3295fc71dd01d04fc0bd3da279763
View on Chainz β†—

Height

#252,141

Difficulty

9.970804

Transactions

2

Size

458 B

Version

2

Bits

09f8869e

Nonce

27,390

Timestamp

11/9/2013, 9:59:39 AM

Confirmations

6,544,168

Merkle Root

c4fe7fd42f44e66ec9f6624962be70b596a69f0bf2ea5f2ad3cb078a7f7aefd4
Transactions (2)
Coinbase3c0c5683c49638…e48393813b4bc5
1 in β†’ 2 out10.0500 XPM141 B
AKcbk49N…GJbKa7j1ASNt3cJa…L5zCqAYM
a953ea8b11325b…b51011160a6578
1 in β†’ 2 out3.7447 XPM226 B
AZy9YnVf…3VpMNryHAJLxRf9N…52B8sgaE
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.

2.655 Γ— 10⁹⁷(98-digit number)
26551565874164543811…28994645114926404800
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
2.655 Γ— 10⁹⁷(98-digit number)
26551565874164543811…28994645114926404799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.655 Γ— 10⁹⁷(98-digit number)
26551565874164543811…28994645114926404801
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
5.310 Γ— 10⁹⁷(98-digit number)
53103131748329087622…57989290229852809599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.310 Γ— 10⁹⁷(98-digit number)
53103131748329087622…57989290229852809601
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
1.062 Γ— 10⁹⁸(99-digit number)
10620626349665817524…15978580459705619199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.062 Γ— 10⁹⁸(99-digit number)
10620626349665817524…15978580459705619201
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
2.124 Γ— 10⁹⁸(99-digit number)
21241252699331635049…31957160919411238399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.124 Γ— 10⁹⁸(99-digit number)
21241252699331635049…31957160919411238401
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
4.248 Γ— 10⁹⁸(99-digit number)
42482505398663270098…63914321838822476799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 252141

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 1002933c774d76590fc820ffd51b3dae13f3295fc71dd01d04fc0bd3da279763

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 #252,141 on Chainz β†—
Circulating Supply:57,614,469 XPMΒ·at block #6,796,308 Β· updates every 60s
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