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Block #31,217

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2013, 10:32:04 PM Β· Difficulty 7.9883 Β· 6,778,636 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7b52468b7c6549405ffe258804ad1978b225a239019e614a70306e6e35fd96f0
View on Chainz β†—

Height

#31,217

Difficulty

7.988303

Transactions

1

Size

197 B

Version

2

Bits

07fd0174

Nonce

37

Timestamp

7/13/2013, 10:32:04 PM

Confirmations

6,778,636

Merkle Root

e33d6274efa0bebb246c4780cde190883cba270a80e4ab5f1ccaa45b502b49eb
Transactions (1)
Coinbasee33d6274efa0be…caa45b502b49eb
1 in β†’ 1 out15.6500 XPM108 B
AKSwr9eU…dLNxuVyn
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.

7.929 Γ— 10⁹²(93-digit number)
79292849079862204489…06925399886352386620
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
7.929 Γ— 10⁹²(93-digit number)
79292849079862204489…06925399886352386619
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.929 Γ— 10⁹²(93-digit number)
79292849079862204489…06925399886352386621
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
1.585 Γ— 10⁹³(94-digit number)
15858569815972440897…13850799772704773239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.585 Γ— 10⁹³(94-digit number)
15858569815972440897…13850799772704773241
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
3.171 Γ— 10⁹³(94-digit number)
31717139631944881795…27701599545409546479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.171 Γ— 10⁹³(94-digit number)
31717139631944881795…27701599545409546481
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
6.343 Γ— 10⁹³(94-digit number)
63434279263889763591…55403199090819092959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.343 Γ— 10⁹³(94-digit number)
63434279263889763591…55403199090819092961
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 31217

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 7b52468b7c6549405ffe258804ad1978b225a239019e614a70306e6e35fd96f0

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 #31,217 on Chainz β†—
Circulating Supply:57,722,911 XPMΒ·at block #6,809,852 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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