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Block #37,610

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 10:53:13 AM Β· Difficulty 8.0511 Β· 6,756,962 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7a16d3543a32ff03ec3934c9cd44e70b70102a28161fbdac27dda22eaf9280a1
View on Chainz β†—

Height

#37,610

Difficulty

8.051094

Transactions

1

Size

201 B

Version

2

Bits

080d147e

Nonce

171

Timestamp

7/14/2013, 10:53:13 AM

Confirmations

6,756,962

Merkle Root

55bd897438739e8800d7802891f415e5e8c56515338c0964202f07b77553fa0f
Transactions (1)
Coinbase55bd897438739e…2f07b77553fa0f
1 in β†’ 1 out15.4100 XPM110 B
AVg3XykK…DTi4Gumt
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.

1.345 Γ— 10⁹⁸(99-digit number)
13455817004472114560…78584998018802466320
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
1.345 Γ— 10⁹⁸(99-digit number)
13455817004472114560…78584998018802466319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.345 Γ— 10⁹⁸(99-digit number)
13455817004472114560…78584998018802466321
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
2.691 Γ— 10⁹⁸(99-digit number)
26911634008944229120…57169996037604932639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.691 Γ— 10⁹⁸(99-digit number)
26911634008944229120…57169996037604932641
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
5.382 Γ— 10⁹⁸(99-digit number)
53823268017888458241…14339992075209865279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.382 Γ— 10⁹⁸(99-digit number)
53823268017888458241…14339992075209865281
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
1.076 Γ— 10⁹⁹(100-digit number)
10764653603577691648…28679984150419730559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.076 Γ— 10⁹⁹(100-digit number)
10764653603577691648…28679984150419730561
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 37610

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 7a16d3543a32ff03ec3934c9cd44e70b70102a28161fbdac27dda22eaf9280a1

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 #37,610 on Chainz β†—
Circulating Supply:57,600,621 XPMΒ·at block #6,794,571 Β· updates every 60s
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