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Block #71,542

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/20/2013, 7:14:01 PM Β· Difficulty 8.9933 Β· 6,753,045 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1ec5a29bb3f88fd1c2d4a1090572fa7f65c87790f3f4d6dbd5cf4f31f2599d44
View on Chainz β†—

Height

#71,542

Difficulty

8.993289

Transactions

1

Size

203 B

Version

2

Bits

08fe4832

Nonce

56

Timestamp

7/20/2013, 7:14:01 PM

Confirmations

6,753,045

Merkle Root

75c648d9a4977e7bfe34b348b1130c0d81387350f529b155f2811acda1ca8877
Transactions (1)
Coinbase75c648d9a4977e…811acda1ca8877
1 in β†’ 1 out12.3500 XPM110 B
APZw681P…Yv3wDWd9
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.

3.211 Γ— 10¹⁰²(103-digit number)
32112165579289359086…70004228278525505750
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
3.211 Γ— 10¹⁰²(103-digit number)
32112165579289359086…70004228278525505749
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.211 Γ— 10¹⁰²(103-digit number)
32112165579289359086…70004228278525505751
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
6.422 Γ— 10¹⁰²(103-digit number)
64224331158578718172…40008456557051011499
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.422 Γ— 10¹⁰²(103-digit number)
64224331158578718172…40008456557051011501
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
1.284 Γ— 10¹⁰³(104-digit number)
12844866231715743634…80016913114102022999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.284 Γ— 10¹⁰³(104-digit number)
12844866231715743634…80016913114102023001
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
2.568 Γ— 10¹⁰³(104-digit number)
25689732463431487268…60033826228204045999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.568 Γ— 10¹⁰³(104-digit number)
25689732463431487268…60033826228204046001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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 8
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 71542

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 1ec5a29bb3f88fd1c2d4a1090572fa7f65c87790f3f4d6dbd5cf4f31f2599d44

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 #71,542 on Chainz β†—
Circulating Supply:57,840,763 XPMΒ·at block #6,824,586 Β· updates every 60s
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