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Block #36,371

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 9:18:52 AM Β· Difficulty 7.9953 Β· 6,769,949 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7f3f1feed2cc068949eb81d9c3c4b0b5182bb2e8d41bb809d92cf931c707a071
View on Chainz β†—

Height

#36,371

Difficulty

7.995317

Transactions

1

Size

200 B

Version

2

Bits

07fecd1f

Nonce

127

Timestamp

7/14/2013, 9:18:52 AM

Confirmations

6,769,949

Merkle Root

78ec1277bc05de86918e2e54283ab9a927423f203a73e25c252057b119119b55
Transactions (1)
Coinbase78ec1277bc05de…2057b119119b55
1 in β†’ 1 out15.6200 XPM110 B
AcTRz1Yt…HVdDtwEc
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.

1.021 Γ— 10⁹⁡(96-digit number)
10213653311705678655…16537875559272422340
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
1.021 Γ— 10⁹⁡(96-digit number)
10213653311705678655…16537875559272422339
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.021 Γ— 10⁹⁡(96-digit number)
10213653311705678655…16537875559272422341
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
2.042 Γ— 10⁹⁡(96-digit number)
20427306623411357310…33075751118544844679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.042 Γ— 10⁹⁡(96-digit number)
20427306623411357310…33075751118544844681
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
4.085 Γ— 10⁹⁡(96-digit number)
40854613246822714620…66151502237089689359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.085 Γ— 10⁹⁡(96-digit number)
40854613246822714620…66151502237089689361
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
8.170 Γ— 10⁹⁡(96-digit number)
81709226493645429241…32303004474179378719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.170 Γ— 10⁹⁡(96-digit number)
81709226493645429241…32303004474179378721
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 36371

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 7f3f1feed2cc068949eb81d9c3c4b0b5182bb2e8d41bb809d92cf931c707a071

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 #36,371 on Chainz β†—
Circulating Supply:57,694,642 XPMΒ·at block #6,806,319 Β· updates every 60s
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